Find the quadratic equation, the sum of whose roots is 7 and the sum of the squares of the roots is 25.

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Q. Find the quadratic equation, the sum of whose roots is 7 and the sum of the squares of the roots is 25.

Yanam BieapBIEAP Intermediate Board 2020Subjective· 2mImportance★★★★★

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Use sum of roots $=7$ and sum of squares $=25$ to get the product of roots, then build $x^2-(\text{sum})x+(\text{product})=0$ .

Let the two roots be $p,q$ .

Given: $p+q = 7$ and $p^2+q^2 = 25$ .

Find $pq$ :

$p^2+q^2 = (p+q)^2 - 2pq \implies 25 = 7^2 - 2pq = 49 - 2pq$ …

Q.Find the quadratic equation, the sum of whose roots is 7 and the sum of the squares of the roots is 25.