Quadratic Equations | MCQs

Explanation

So in this way the next number in the sequence, 0, 3, 8, 15, 24, 35

From the given series the logic is adding odd numbers in the series

0 + 3 = 3

3 + 5 = 8

8 + 7 = 15 

15 + 9 = 24

24 + 11 = 35

Explanation

In a quadratic equation, the highest power of the variable (usually x) is 2, as in the general form ax² + bx + c = 0.

Explanation

Since 3 is a solution, plug x = 3 into the equation:

3(3)^2 + (k - 1)(3) + 9 = 0

27 + 3k - 3 + 9 = 0

3k + 33 = 0

3k = -33

k = -11

Explanation

The quadratic equation whose roots are reciprocal of:

2x2 + 5x + 3 = 0 can be obtained by replacing x by 1/x.

Hence, 2(1/x)2 + 5(1/x) + 3 = 0

=> 3x^2 + 5x + 2 = 0

Explanation

In ax² + bx + c = 0, if > 0, b > 0, and c > 0, the parabola opens upward and lies entirely above the x-axis unless discriminant D = b² - 4ac ≥ 0.

If real roots exist, they are negative because both b and c are positive.

Explanation

Let's directly calculate:

x - y = 5

x² - y² = 65

(x + y)(x - y) = 65

(x + y)(5) = 65

x + y = 13

Solving these equations:

x - y = 5

x + y = 13

Adding both: 2x = 18

x = 9

y = 4

Let's check:

9 - 4 = 5

9² - 4² = 81 - 16 = 65

Explanation

(x - 2)(x + 3) = 0

This implies:

x - 2 = 0 or x + 3 = 0

x = 2 or x = -3

Explanation

Given that x = 3 is a solution to the equation:

x² + rx - 20 = 4

Substitute x = 3 into the equation:

(3)² + r(3) - 20 = 4

Simplify:

9 + 3r - 20 = 4

Combine like terms:

3r - 11 = 4

Add 11 to both sides:

3r = 15

Divide by 3:

r = 5

Explanation

Given roots are 3 and -5.

The quadratic equation is:

(x - 3)(x + 5) = 0

x^2 + 2x - 15 = 0

Explanation

Let "x" be the number.

Three-fourths of the number is (3/4)x.

When we multiply the number by three-fourths of itself,

we get: x * (3/4)x = 10700.

This simplifies to (3/4)x² = 10700.

Solving for x, we get x = 70.