Question

If alpha and beta are zeroes of x^2+7x+7 then find the value of alpha^2 + beta^2

Answer 1

Answer:

35

Note:

• If A and B are the zeros of the a quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , A•B = c/a

• If A and B are the zeros of any quadratic polynomial , then it is given as ;

x² - (A+B)x + A•B.

Solution:

Here,

The given quadratic polynomial is:

x² + 7x + 7.

Clearly,

a = 1

b = 7

c = 7

Thus,

Sum of zeros = -b/a

=> α + ß = -7/1 = -7

Also,

Product of zeros = c/a

=> αß = 7/1 = 7

Now,

α² + ß² = (α + ß)² – 2αß

= (-7)² – 2×7

= 49 – 14

= 35

Hence,

The required value of the α² + ß² is 35 .