Quadratic Equation Test

Result

Quadratic Equation Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

If the equation x² – m (2x – 4) + 5 = 0 has equal roots, which of the following is the value of m?

A
5

B
4

C
2

D
1

Solution

x² - m (2x - 4) + 5 = 0
x² - 2mx + 4m + 5 = 0

For equal roots, b² - 4ac = 0
⇒(- 2m)² - 4 (4m + 5) = 0
4 (m² - 4m - 5) = 0

(m - 5) (m + 1) = 0
Thus, m = 5 is the answer.
Question 2
1 / -0

If the roots of the equation 4x² – 4px + 7p – 12 = 0 are equal, find the value of p.

A
3 or 5

B
2 or 5

C
3 or 4

D
2 or 3

Solution

4x² - 4px + 7p - 12 = 0

Roots are equal. Therefore, b² - 4ac = 0
⇒ (- 4p)² - 4(4) (7p - 12) = 0
16 (p² - 7p + 12) = 0

(p - 3) (p - 4) = 0
Hence, p = 3, p = 4.
Question 3
1 / -0

Only one of the roots of ax² + bx + c = 0, a ≠ 0, is zero, if

A
c = 0

B
c = 0, b ≠ 0

C
b = 0, c = 0

D
b ≠ 0, c ≠ 0

Solution

When one root is zero and the other is non-zero, then
a(0)² + b(0) + c = 0
i.e. c = 0
Now, b ≠ 0 because if b = 0, then both the roots will be equal to 0.
As the equation will become
ax²= 0
Or x = 0, 0 (not possible, as both the roots are zero)
i.e. c = 0 and b ≠ 0