Question

Find a and b if x = 0 and x = -1 are the zeros of p(x) = 2x³ - 3x² + ab + b..​

Answer 1

CORRECT question :–

• Find a and b if x = 0 and x = -1 are the zeros of p(x) = 2x³ - 3x² + ax + b.

ANSWER :–

GIVEN :–

• Zero's of Polynomial p(x) = 2x³ - 3x² + ax + b are x = 0 and x = -1 .

TO FIND :–

• Value of 'a' and 'b' = ?

SOLUTION :–

• Zeros of polynomial always satisfy the polynomial .

• So that –

• When x = 0 :–

$\\ \implies \sf p(0) = 0$

$\\ \implies \sf 2 {(0)}^{3} - 3( {0)}^{2} + a(0) + b = 0$

$\\ \implies \large{ \boxed{ \sf b = 0 }}$

• When x = -1 :–

$\\ \implies \sf p( - 1) = 0$

$\\ \implies \sf 2 {( - 1)}^{3} - 3( { - 1)}^{2} + a( - 1) + b = 0$

$\\ \implies \sf - 2 - 3 - a + b = 0$

$\\ \implies \sf b - a = 5$

• Put the value of 'b' –

$\\ \implies \sf 0 - a = 5$

$\\ \implies \large{ \boxed{ \sf a = - 5}}$

• Hence , The value of 'a' is -5 and value of 'b' is 0.

Answer 2

Correct Given:

• p(x) = 2x³ - 3x + ax + b
• x = 0 & x = -1
• p(-1) = 0 & p(0) = 0

To find:

• a , b

Solution:

p(x) = 2x³ - 3x² + ax + b

Putting x = -1

→ p(-1) = 2(-1)³ - 3(-1)² + a(-1) + b

→ -2 - 3 - a + b = 0

→ b - a = 5 ………… eq 1

______________________

Putting x = 0

→ p(0) = 2(0)³ - 3(0)² + a(0) + b

→ b = 0

______________________

Substituting b = 0 in eq. 1

♦ 0 - a = 5

♦ a = -5

Hence, a = -5 & b = 0