In-a-quadratic-equation-ax-2-bx-c-0-a-b-c-are-distinct-primes-and-the-product-of-the-sum-of-the-roots-and-product-of-the-roots-is-91-9-Find-the-absolute-value-of-difference-between-the-sum-o

Question Number 76401 by saupriyadip571@gmail.com last updated on 27/Dec/19

In a quadratic equation {a x}^{2} - b x + c = 0,

a, b, c are distinct primes and the product

of the sum of the roots and product of

the roots is \frac{91}{9} . Find the absolute value of

difference between the sum of the roots

and the product of the roots .

Answered by mr W last updated on 27/Dec/19

s a y r o o t s a r e α, β .

α + β = \frac{b}{a}

α β = \frac{c}{a}

g i v e n : (α + β) α β = \frac{91}{9}

\Rightarrow \frac{b c}{a^{2}} = \frac{91}{9} = \frac{13 \times 7}{3^{2}}

s i n c e a, b, c a r e p r i m e,

\Rightarrow a = 3, b = 13 (o r 7), c = 7 (o r 13)

X = (α + β) - α β = \frac{b - c}{a} = \frac{13 - 7}{3} = 2

\Rightarrow a n s w e r i s 2 .

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