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If one root of the equation \( \Large x^{2}+px+12=0 \) is 4, while the equation \( \Large x^{2}-7x+q=0 \) has equal roots, then the value of 'g' is:


A) \( \Large \frac{49}{4} \)

B) 12

C) 3

D) 4

Correct Answer:
A) \( \Large \frac{49}{4} \)

Description for Correct answer:

Since, 4 is one the roots of equation \( \Large x^{2}+px+12=0 \) so it must satisfies the equation

\( \Large \therefore 16 + 4P + 12 = 0\)

\( \Large 4 \pi = -28 \)

=> P = -7

The other equation is \( \Large x^{2}-7x+q=0 \) whose roots are equal lets roots are \( \Large \alpha \) and \( \Large \alpha \) of above equation

\( \Large \therefore Sum\ of\ roots = \alpha + \alpha = \frac{7}{1} \)

=> \( \Large 2 \alpha = 7 => \alpha =\frac{7}{2} \)

and product of roots = a . a = q.

\( \Large \alpha ^{2} = q \)

=> \( \Large \left(\frac{7}{2}\right)^{2}=q => q=\frac{49}{4} \)


Part of solved Quadratic Equations questions and answers : >> Elementary Mathematics >> Quadratic Equations




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