Question

if
$\alpha + \beta$
are the zeros of polynomial p(X).
${3x}^{2} - 12x + 15$find the value of
$\alpha {}^{2} + \beta {}^{2 }$
​

Answer 1

Answer:

α²+β²=6

Step-by-step explanation:

α and β are the zeros of  p(x)=3x²-12x+15.

In the polynomial,

a=3, b= -12 & c=15

We know, α+β= -b/a

⇒α+β= -(-12)/3

⇒α+β= 12/3

⇒α+β=4------------------(i)

Now,

αβ= c/a

⇒αβ=15/3

⇒αβ=5--------------------(ii)

α²+β²=(α+β)²-2αβ

⇒α²+β²=4²-2*5                                          [∴ From (i) and (ii)]

⇒α²+β²=16-10

⇒α²+β²=6