Question

If aandß are the zeroes of the polynomial x2 + 5x + 6, then frame the
quadratic polynomial whose zeroes are:1 + B and 1 + «​

Answer 1

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial p(x) = x² + 5x + 6

To Find -

• A quadratic polynomial whose zeroes are 1 + α and 1 + β

Now,

→ x² + 5x + 6

By middle term splitt :-

→ x² + 2x + 3x + 6

→ x(x + 2) + 3(x + 2)

→ (x + 3)(x + 2)

Zeroes are -

→ x + 3 = 0 and x + 2 = 0

→ x = -3 and x = -2

New Zeroes are -

• 1 + α

→ 1 + (-3) = -2

And

• 1 + β

→ 1 + (-2) = -1

• Sum of new zeroes is

→ -2 + (-1) = -b/a

→ -3/1 = -b/a ...... (i)

And

• Product of new zeroes is

→ -2 × -1 = c/a

→ 2/1 = c/a ..... (ii)

Now, From (i) and (ii), we get :-

a = 1

b = 3

c = 2

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (3)x + 2

→ x² + 3x + 2

Hence,

The new quadratic polynomial is x² + 3x + 2.