Question

if alpha and beta are zeroes of quadratic polynomial ax²+bx+c, evaluate α²+β²​

Answer 1

Answer:

α² + ß² = b²/a² - 2c/a

Note:

★ The possible values of variable for which the polynomial becomes zero are called its zeros.

★ A quadratic polynomial can have atmost two zeros.

★ If α and ß are the zeros of the 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 :

ax² + bx + c .

Also,

α and ß are the zeros of the given quadratic polynomial , thus ;

α + ß = -b/a

αß = c/a

Now,

=> (α + ß)² = α² + ß² + 2αß

=> α² + ß² = (α + ß)² - 2αß

= (-b/a)² - 2(c/a)

= b²/a² - 2c/a

Hence,

α² + ß² = b²/a² - 2c/a