Question

If alpha and beta are zeroes of the polynomial x2 - 6x + a.Find the value of a if beta = -2

Answer 1

Answer:

alpha + beta = -b/ a

alpha = 6 - (-2)

alpha= 8

alpha × beta = a

8 ×(-2)= -16

Answer 2

Answer:

a = –16

Note:

If α and ß are the zeros of a quadratic polynomial Ax² + Bx + C , then ;

Sum of zeros , (α + ß) = -B/A

Product of zeros , αß = C/A

Solution:

Here,

The given quadratic polynomial is :

x² - 6x + a.

Clearly,

A = 1

B = -6

C = a

Also,

It is given that , α and ß are the zeros of the given quadratic polynomial.

Thus,

=> Sum of zeros = -B/A

=> α + ß = -(-6)/1

=> α + ß = 6

=> α + (-2) = 6 { Given : ß = -2 }

=> α - 2 = 6

=> α = 6 + 2

=> α = 8 ---------(1)

Also,

=> Product of zeros = C/A

=> αß = a/1

=> αß = a

=> α×(-2) = a

=> 8×(-2) = a { using eq-(1) , a = 8 }

=> -16 = a

=> a = -16

Hence,

The required value of a is –16 .