Quant Quadratic

If α and β are the roots of the equation x^2 + px + q = 0

If α and β are the roots of the equation x² + px + q = 0, then what is α² + β² equal to?

p² – 2q
q² – 2p
p² + 2q
q² – q

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

-4, -3
6, 1
4, 3
-6, -1

The value of x^2 - 4x + 11 can never be less than

The value of x2 - 4x + 11 can never be less than

7
8
11
22

If the roots of the equation Ax^2 + Bx + C = 0 are -1 and 1

If the roots of the equation Ax² + Bx + C = 0 are -1 and 1, then which one of the following is correct?

A and B are both positive
A and C are both negative
A and C are of opposite sign
A and C are both zero

If a - b = 4 and a^2 + b^2 = 40 where a and b are positive integers

If a - b = 4 and a² + b² = 40 where a and b are positive integers, where a and b are positive integers, then a³ + b⁶ is equal to

264
280
300
324

The sign of the quadratic polynomial ax^2 + bx + c is always

The sign of the quadratic polynomial ax² + bx + c is always positive if

a is positive and b² - 4ac ≤ 0.
a can be any real number and b² - 4ac ≤ 0.
a can be any real number and b² - 4ac ≥ 0.
a is positive and b² - 4ac ≥ 0.

In solving a problem, one student makes a mistake in the coefficient

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was:

x² + 10x + 9 = 0
x² - 10x + 16 = 0
x² - 10x + 9 = 0
x² + 10x + 16 = 0

The expression 2x^3 + x^2 - 2x - 1 = 0 is divisible by

The expression 2x³ + x² - 2x - 1 = 0 is divisible by

2x - 1
2x + 1
x + 2
x - 2

If x^2 = 6 + √(6 + √(6 + √(6 + ....∞)), then what is one of the values

If x² = 6 + √(6 + √(6 + √(6 +....∞)), then what is one of the values of x equal to?

3
4
5
6

If α and β are the roots of the equation x^2 - x - 1 = 0

If α and β are the roots of the equation x² - x - 1 = 0, then what is (α² + β²)/((α² - β²)(α - β))

2/5
4/5
3/5
1/5

If the roots of the equation (a2 - bc)x2 + 2(b2 - ac)x + (c2 - ab) = 0 are equal

If the roots of the equation (a² - bc)x² + 2(b² - ac)x + (c² - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?

a³ + b³ + c³ = 0
a³ + b³ + c³ = 3abc
a² + b² + c² = 0
a + b + c = abc

Largest value of min(2 + x^2, 6 - 3x), when x > 0, is

Largest value of min(2 + x², 6 - 3x), when x > 0, is

1
2
3
4

A quadratic function f(x) attains a maximum of 3 at x = 1

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value f(x) at x = 10?

-180
-159
-110
-119

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax²+ bx + 1 = 0 having real roots is

6
7
10
12

Let p and q be the roots of the quadratic equation x^2 - (α-2)x - α - 1 = 0

Let p and q be the roots of the quadratic equation x² - (α - 2)x - α - 1 = 0. What is the minimum possible value of p² + q²?

0
3
4
5

The number of roots common between the two equations x^3 + 3x^2 + 4x + 5 = 0

The number of roots common between the two equations x³ + 3x² + 4x + 5 = 0 and x³ + 2x² + 7x + 3 = 0 is

0
1
2
3

One root of x^2 + kx - 8 = 0 is square of the other. Then the value of k is

One root of x² + kx - 8 = 0 is square of the other. Then the value of k is

2
-2
8
-8

What is the value of m which satisfies 3m^2 - 21m + 30

What is the value of m which satisfies 3m² - 21m + 30 < 0?

m < 2 or m > 5; 2 < m < 5
2 < m < 5
m < 2 or m > 5
m > 2

Which of the following values of x do not satisfy the inequality x^2 - 3x + 2 > 0 at all

Which of the following values of x do not satisfy the inequality x² - 3x + 2 > 0 at all?

0 ≥ x ≥ –2
0 ≤ x ≤ 2
–1 ≥ x ≥ –2
1 ≤ x ≤ 2

The minimum possible value of the sum of the squares of the roots

The minimum possible value of the sum of the squares of the roots of the equation x² + (a + 3)x - (a + 5) = 0 is

1
2
3
4