Question

21. If a and B are zeroes of the quadratic polynomial x2 - 6x + a; find the value of 'a' if
3a + 2B = 20.​

Answer 1

Answer:

$\bold\red{a=-16}$

Step-by-step explanation:

Given,

A quadratic equation :

${x}^{2} - 6x + a = 0$

Also,

A and B are roots of the equation.

Therefore,

sum of roots, A + B = 6

Product of roots, AB = a

=> A = 6- B .........(i)

But,

it is given that,

3A + 2B = 20

Now,

Putting the value of 'A' from eqn (i)

we get,

=> 3 (6 - B ) + 2B = 20

=> 18 -3B + 2B = 20

=> 3B - 2B = 18 - 20

=> B = -2

Therefore,

a = 6 - B = 6 - (-2)

=> A = 8

Hence,

a = AB = 8 × (-2) = -16

Answer 2

Answer:

here a is replaced with alpha and b is replaced with beta