Question

If α and β are the zeroes of quadratic polynomial x 2 -2x-8 then form a quadratic polynomial whose zeroes are 3α and 3β

Answer 1

α,β are the zeros of x²-2x-8=0. then, α+β=-(-2/1)=2 and
α×β=-8/1=-8
now, 3α+3β=3(α+β)=3×2=6 and 3α×3β=9αβ=9×-8=-72
the required quadratic polynomial is:
x²-(sum of the roots)x+product of the roots=0
or, x²-6x-72=0

Answer 2

If α and β are the zeroes of quadratic polynomial x 2 - 2x - 8 then

α+β= -b/a = -(-2/1) = 2

and

αβ= c/a = (-8/1) = -8

Now we have to form a Quadratic Equation having zeroes 3α and 3β

So, first sum of zeroes

3α + 3β

= 3(α+β)

= 3(2)

= 6

and product of zeroes

3α.3β

=9αβ

= 9(-8)

= -72

So, the format of Quadratic Equation

kx²-(α+β)x+αβ=0

replacing values

=kx²-(6)x+(-72)      ( k=1)

=x² - 6x -72