Question

f α and β are zeroes of the quadratic polynomial x2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20

Answer 1

Please refer the image for your answer...

Answer 2

From the given expression

→ $\alpha +\beta =-\frac{-6}{1}$

→ $\alpha +\beta =6$

However, we are given value of $3\alpha +2\beta =20$

→ $3\alpha +2\beta=20$

→ $(1+2)\alpha +2\beta=20$

→ $\alpha +(2\alpha +2\beta )=20$

→ $\alpha +12=20$

→ $\boxed{\text{The value of }\alpha\text{ is 8.}}$

However, you have 2 choices here.

1. Since x=8 sets the expression value to 0

→ $64-48+a=0$

→ $16+a=0$

→ $\boxed{\text{The value of }a\text{ is -16.}}$

2. From the given equation $\alpha \beta =\frac{a}{1}$

Since we know the value of α is 8, the value of β becomes -2.

→ $\boxed{\text{The value of }a\text{ is -16.}}$