Question

If a and b are the zeroes of polynomial x^2 + x - 2 find a polynomial whose zeroes are 3a + 1 and 3b + 1​

Answer 1

$\huge \fbox \pink{SOLUTION :-}$

GIVEN,

x² + x - 2 is a polynomial with a and b as its zeros.

TO FIND,

a polynomial whose zeroes are 3a + 1 and 3b + 1.

SOLUTION,

=> x² + x - 2

by splitting the middle terms.

=> x² - x + 2x - 2

=> x(x - 1) + 2(x - 1)

=> (x - 1)(x + 2)

Hence, a = 1 and b = -2 are the Zeroes the of polynomial x² + x - 2.

Putting the value of a and b on 3a + 1 and 3b + 1.

=> 3a + 1

=> 3(1) + 1

=> 3 + 1

=> 4

=> 3a + 1 = 4

=> 3b + 1

=> 3(-2) + 1

=> -6 + 1

=> -5

=> 3b + 1 = -5

Here,

Sum of Zeroes (S) = 4 + (-5) = 4 -5 = -1

Product of Zeroes (p)= 4 × -5 = -20

We know that,

p(x) = k(x² - Sx +p)

p(x) = x² +x -20

Hence, x² + x - 20 is a polynomial whose zeroes are 3a + 1 and 3b + 1.