Question

if alpha and beta are roots of quadratic equation x^2+px+q=0, then find the value of alpha square and beta square ​

Answer 1

Answer:

p^2-2q

Step-by-step explanation:

a^2+b^2=[a+b]^2-2ab=p^2-2q

Answer 2

The value is

$\alpha^2+\beta^2=p^2-2q$

Step-by-step explanation:

The given quadratic equation is x²+px+q=0

It has been given that α and β are the roots of this equation.

Hence, sum of roots is given by

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

And product of roots is given by

$\frac{c}{a}\\\\\alpha\cdot\beta=q$

Now, using the below rule

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

Substituting the known values, we get

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

#Learn More:

If one root of the polynomial f(x)=X2 +5x+k is reciprocal of the other.find the value of k and verify it.

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