Question

If x = 2 and x = 3 are zeros of the quadratic polynomial x2 + ax + b, the values of a and b respectively are​

Answer 1

Step-by-step explanation:

Given:If x = 2 and x = 3 are zeros of the quadratic polynomial x2 + ax + b.

To find:The values of a and b are ?

Solution:

Tip: Apply factor theorem.

Step 1: Put x=2 in x²+ax+b

$( {2)}^{2} + 2a + b = 0 \\ \\ 2a + b = - 4 \: \: \: ...eq1$

Step 2: Put x=3

$( {3)}^{2} + 3a + b = 0 \\ \\ 3a + b = - 9 \: \: \: ...eq2$

Step 3: Subtract both equations

$2a + b = - 4 \\ 3a + b = - 9 \\ ( - ) \: ( - ) \: ( + ) \\ - - - - - - \\ - a = 5 \\ \\ a = - 5$

Step 4: Put the value of a in eq1

$2( - 5) + b = - 4 \\ \\ - 10 + b = - 4 \\ \\ b = - 4 + 10 \\ \\ b = 6$

Final answer:

Value of a and b are -5 and 6 respectively.

Hope it helps you.

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