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The roots of $x^{2} - 7 x + 12 = 0$ are alpha and beta. The quadratic equation whose roots are alph $a^{2}$ and bet $a^{2}$ is:

Class 10Sum and Product of RootsAlgebra — Quadratics

A $x^{2} - 25 x + 144 = 0$
B $x^{2} - 49 x + 144 = 0$
C $x^{2} - 25 x + 12 = 0$
D $x^{2} + 25 x + 144 = 0$

Step-by-Step Solution

Sum 7, product 12. alph

a^{2}

+ bet

a^{2} = 49 - 24 = 25

; alph

a^{2}

bet

a^{2} = 1 2^{2} = 144

. Equation:

x^{2} - 25 x + 144 = 0

.

Answer: A)

x^{2} - 25 x + 144 = 0

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