quadratic equation 4x² ? 12x

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Q.
Assertion (A): The quadratic equation $4 x ² - 12 x + 9 = 0$ has repeated roots.

Reason (R): The quadratic equation $a x ² + b x + c = 0, a \neq 0$ , has equal roots if D > 0.

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true

Ans.
(3)

Given, $4 x ² - 12 x + 9 = 0 . D i s c r i m i n a n t, D = (- 12) ² - 4 \times 4 \times 9 = 144 - 144 = 0 .$

Hence, the equation has equal (repeated) roots. Assertion (A) is true but Reason (R) is false.

Solution

Q.
Assertion (A): The quadratic equation $4 x ² - 12 x + 9 = 0$ has repeated roots.

Reason (R): The quadratic equation $a x ² + b x + c = 0, a \neq 0$ , has equal roots if D > 0.

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true

Ans.
(3)

Given, $4 x ² - 12 x + 9 = 0 . D i s c r i m i n a n t, D = (- 12) ² - 4 \times 4 \times 9 = 144 - 144 = 0 .$

Hence, the equation has equal (repeated) roots. Assertion (A) is true but Reason (R) is false.

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Solution

Q. Assertion (A): The quadratic equation 4x² − 12x + 9 = 0 has repeated roots. Reason (R): The quadratic equation ax² + bx + c = 0, a ≠ 0, has equal roots if D > 0.

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true

Ans. (3) Given, 4x² − 12x + 9 = 0. Discriminant, D = (−12)² − 4×4×9 = 144 − 144 = 0. Hence, the equation has equal (repeated) roots. Assertion (A) is true but Reason (R) is false.

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Q.
Assertion (A): The quadratic equation $4 x ² - 12 x + 9 = 0$ has repeated roots.

Reason (R): The quadratic equation $a x ² + b x + c = 0, a \neq 0$ , has equal roots if D > 0.

Ans.
(3)

Given, $4 x ² - 12 x + 9 = 0 . D i s c r i m i n a n t, D = (- 12) ² - 4 \times 4 \times 9 = 144 - 144 = 0 .$

Hence, the equation has equal (repeated) roots. Assertion (A) is true but Reason (R) is false.