Assertion :A quadratic equation has a root $8 - 3 i$ , then sum of roots of the quadratic equation is $16$ . Reason: If one root of the quadratic equation $a x^{2} + b x + c = 0$ $(a \neq 0, a, b, c \in R)$ is $8 - 3 i$ , then other root has to be $8 + 3 i$ .

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect, Reason is correct

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Solution

The correct option is D Assertion is incorrect, Reason is correct
Complex roots occur in conjugates, when the coefficients of the terms of the quadratic equation are real.
Hence, Reason is correct.
However, in the assertion it is not given whether the coefficients are real or not.
Hence, assertion is not true always.

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Similar questions

Q. Assertion (A)
The equation x² + x + 1 = 0 has both real roots.

Reason (R)
The equation ax2 + bx + c = 0, (a ≠ 0) has both real roots, if (b2 − 4ac) > 0.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
If −5 is a root of

2 x^{2} + 2 p x - 15 = 0 and p (x^{2} + x) + k = 0

has equal roots, then

k = \frac{7}{8} .

Reason (R)
The equation

a x^{2} + b x + c = 0, a \neq 0

has equal roots, if

(b^{2} - 4 a c) = 0 .

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
If

p x^{2} - 2 x + 2 = 0

has real roots, then

p \leq \frac{1}{2} .

Reason (R)
The equation

(a^{2} +^{b}) x^{2} + 2 (a c + b d) x + (c^{2} + d^{2}) = 0

has no real root, if ad ≠ bc.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Assertion (A) Order of the reaction can be zero or fractional.

Reason (R) We cannot determine order from balanced chemical equation.

(a) Both assertion and reason are correct and the reason is correct explanation of assertion
(b) Both assertion and reason are correct, but reason does not explain assertion.
(c) Assertion is correct, but reason is incorrect
(d) Both assertion and reason are incorrect
(e) Assertion is incorrect but reason is correct.

Assertion: All the points (1, 0), (-1, 0), (2, 0) and (5, 0) lie on the x – axis.

Reason: Equation of the x – axis is y = 0
Now, choose the correct option.

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Assertion :A quadratic equation has a root 8−3i, then sum of roots of the quadratic equation is 16. Reason: If one root of the quadratic equation ax2+bx+c=0 (a≠0,a,b,c∈R) is 8−3i, then other root has to be 8+3i.

Assertion :A quadratic equation has a root $8 - 3 i$ , then sum of roots of the quadratic equation is $16$ . Reason: If one root of the quadratic equation $a x^{2} + b x + c = 0$ $(a \neq 0, a, b, c \in R)$ is $8 - 3 i$ , then other root has to be $8 + 3 i$ .