The quadratic equation with real coefficients whose one root is 7… - Vidyadip

MCQ

The quadratic equation with real coefficients whose one root is $7 + 5i$, will be

✓
${x^2} - 14x + 74 = 0$
B
${x^2} + 14x + 74 = 0$
C
${x^2} - 14x - 74 = 0$
D
${x^2} + 14x - 74 = 0$

✓

Answer

Correct option: A.

${x^2} - 14x + 74 = 0$

a
(a) Let $\alpha = 7 + 5i$, then its conjugate $\beta = 7 - 5i$, so required equation is given by ${x^2} - (\alpha + \beta )x + \alpha \beta = 0$

==> ${x^2} - (14)x + (49 + 25) = 0$

==> ${x^2} - 14x + 74 = 0$

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