Question

if α and β are the two zeros of polynomial x²-6x-a find a if 3α+3β=2​

Answer 1

Correct Question

if α and β are the two zeros of polynomial x²-6x-a find a if 3α+2β=20

To find

find a if 3α+3β=20

Solution

Given equation

x² - 6x - a

Sum of zeros

α+β = -b/a = -(-6)/1

α+β = 6 ----(i)

Now,

Product of zeros

αβ = c/a = -a/1

αβ = -a ---(ii)

3α+2β=20 ---(iii)

From (i)

=> α + β = 6

=> α = 6-β

By substitution method

By substitution method substitute the value of α in equation (iii)

=> 3α+2β=20

=> 3(6-β) + 2β = 20

=> 18 - 3β + 2β = 20

=> 18 - 20 = β

=> β = -2

Putting the value of β in equation (i)

=> α = 6-β

=> α = 6-(-2) = 6+2 = 8

So,

From (ii)

Putting the value of α and β

=> αβ = -a

=> 8×(-2) = -a

=> -16 = -a

=> a = 16