Question

if alpha and beta are the zeroes of the polynomial p(x) = 3x2 - 14x +15 ,find the value of alpha square + beta square

Answer 1

I hope it will help you

Answer 2

The value of $\alpha^2+\beta^2=\frac{106}{9}$

Step-by-step explanation:

$p(x) = 3x^2 - 14x +15$

$\alpha$ and $\beta$ are zeroes

General equation : $ax^2+bx+c=0$

Sum of zeroes = $\frac{-b}{a}$

Product of zeroes = $\frac{c}{a}$

Sum of zeroes of given equation : $\alpha+\beta=\frac{14}{3}$

Product of zeroes of given equation : $\alpha\beta =\frac{15}{3}=5$

we are supposed to find $\alpha^2+\beta^2$

Formula : $(a+b)^2=a^2+b^2+2ab\\(a+b)^2-2ab=a^2+b^2$

$(\alpha+\beta)^2-2 \alpha \beta=\alpha^2+\beta^2$

Substitute the values:

$(\frac{14}{3})^2-2(5)=\alpha^2+\beta^2\\\\\frac{106}{9}=\alpha^2+\beta^2$

Hence the value of $\alpha^2+\beta^2=\frac{106}{9}$

#Learn more:

If alpha and beta are the zeroes of the polynomial p(x) = 3x2 - 14x +15 ,find the value of alpha square + beta square

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