Question

Find the quadratic polynomial whose zereos are 5 and 2

Answer 1

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Answer 2

Let $\alpha=5$ $\beta=2$ be the zeros of a quadratic polynomial.

$p(x) = ax^{2} + bx + c=0$

$\red{p(x) = x^{2}+\frac{-b}{a} + \frac{c}{a} = 0}$

We know that:-

$\alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a}$

Hence:-

$5 + 2 = \frac{ - b}{a} ~and \: 5 \times 2 = \frac{c}{a} \\ 7 = \frac{ - b}{a} ~and \: 10 = \frac{c}{a}$

$p(x)=x^{2}+(\frac{-b}{a} )+ \frac{c}{a} = 0$

$p(x) = x^{2}-\frac{b}{a} + \frac{c}{a} = 0$

$\red{p(x) = x^{2} - 7x + 10 = 0}$