The standard form of a quadratic equation in one variable is —
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138 questions · 18 sections
The standard form of a quadratic equation in one variable is —
The values of variables for which both sides of an equation are equal are called —
In , which condition must hold?
The two roots of are given by —
The expression in the quadratic formula is called —
For with , the values of are —
For with , the roots are —
The roots of are —
The discriminant of is —
The roots of are —
The roots of are —
The roots of are —
If and is a perfect square, the roots of are —
If but not a perfect square, the roots are —
If , the roots are —
When , each root equals —
If , the two roots are —
Which condition gives real, unequal and irrational roots?
Consider the following statements about a quadratic with real coefficients:
Nature of the roots of is —
The roots of are —
The discriminant of is —
The roots of are —
The roots of are —
The roots of are —
The roots of are —
The roots of are —
The roots of are —
The roots of are —
In an equation involving square roots, freeing the radical sign by squaring may introduce —
Roots that arise from the squared equation but do not satisfy the original equation are called —
After solving a radical equation by squaring, we must —
The solution of is —
The solutions of are —
The acceptable solution of is —
In , the value is rejected because —
The solutions of are —
To solve , the most useful substitution is —
The solutions of are —
The solution of is —
To begin solving , a useful substitution is —
To solve , replacing gives —
Squaring an equation involving radicals usually requires —
An equation in which the unknown variable exists as an exponent is called —
Which of the following is an indicial equation?
The property used to solve requires —
If and , then —
expressed as a power of is —
expressed as a power of is —
The solution of is —
The solution of is —
The solution of is —
The solution of is —
The solution of is —
The solution of is —
The substitution used in solving is —
The solution of is —
After substituting , the equation becomes —
The solutions of are —
A pair is a solution of a system if —
The solutions of are —
From and , factoring after subtraction gives —
One solution of is —
One solution of is —
From together with , we obtain —
The solutions of the system in the previous question are —
The sum of areas of two square regions is sq m and the rectangle on their sides has area sq m. The sides are —
Twice the breadth of a rectangle is m more than its length and the area is sq m. The length is —
A two-digit number divided by the product of its digits gives quotient , and adding reverses the digits. The number is —
Sum of areas of two squares is sq m and the rectangle on their sides has area sq m. The sides are —
The sum of the squares of two positive numbers is and their product is . The numbers are —
The diagonal of a rectangle is m. The rectangle whose sides are the sum and difference of the original sides has area sq m. The original sides are —
The sum of squares of two numbers is and their product is . The difference of their squares is —
A rectangle has area sq m. Another rectangle whose length and breadth are m and m more respectively has area sq m. The first rectangle's sides are —
Twice the breadth of a rectangle is m more than its length and the area is sq m. The length and breadth are —
The perimeter of a rectangle is m more than the sum of its diagonals. If the area is sq m, the length and breadth are —
A two-digit number divided by the product of its digits gives quotient , and adding reverses the digits. The number is —
A rectangular garden has perimeter m and one diagonal m. The side of a square enclosing an equal area is —
A rectangular field has area sq m and its semi-perimeter is m more than a diagonal. The length and breadth are —
A rectangle bounded by the sides and of two squares has area . The maximum possible sum of the areas of the squares (with positive integer sides) is —
To solve graphically, the values of where —
The graph of crosses the X-axis at —
The graphical solution of gives —
The graph of touches the X-axis at —
The roots of from the graph are —
The approximate roots of from the graph are —
The roots of from the graph are —
For with , the value of is —
For with , the discriminant is —
The nature of roots of is —
Given and , the values of are —
What is the value of in if compared with ?
A root of the equation is —
A root of the system is —
The sum of a number and its multiplicative inverse is . Consider:
If , then —
The graphical solution of is —
The graphical solution of is —
The graphical solution of is —
The graphical solution of is —
The graphical solution of is —
The graphical solution of is —
"Twice the square of a number is less by than times the number." The equation is —
The roots of by formula are —
"Five times the square of a number is greater by than times of the number." The roots from the graph are —
Mr. Ashfaque Ali's land has area hectare. Half its perimeter is m greater than one diagonal. The length and breadth of his land are —
Mr. Shyam buys one-third of Mr. Ashfaque's land. The area of Shyam's land is —
Could the product of the sum of digits of five consecutive integers and the sum of digits of the next five consecutive integers be ?
For a rectangle with length breadth cm and the units digit of the area equal to , can any side be a perfect square?
How many times in a day are the hands of a clock in a straight line but in opposite directions?
How many times in a day are the hands of a clock perpendicular to each other?
Which one is the solution of the equation ?
If the sum of a number and its multiplicative inverse is , consider:
The difference of the squares of two positive integers is and their product is . The sum of the squares of the two numbers is —
The two numbers in the previous question are —