Question

if a and ß are the zeros of p(x) =x square +x-1 , then find a square ß+aß square​

Answer 1

Given :-

a and ß are zeroes of the p ( x ) = x² + x - 1 .

To Find :-

The Value of a²ß + aß²

Solution :-

• A simple Quadratic equation is in the form of ax² + bx + c = 0 .
• Sum of zeroes of the above equation is given by -b/a .
• Product of zeroes of the above equation is given by c/a.

Solution :-

p ( x ) = x² + x - 1

For zeroes p ( x ) = 0 . So ,

=> x² + x - 1 = 0

It is in the form of ax² + bx + c = 0 .

Where , a = 1 , b = 1 , c = -1 .

=> Let , 1st zero of the given = a

=> 2nd zero of the given = ß

Now , a + ß = -b/a = -1/1 = -1

=> a × ß = c/a = -1/1 = -1

Now , we have to find the value of a²ß + aß² which can also be written as :-

=> aß ( a + ß )

=> Putting values we get ,

=> -1 × ( -1 )

=> 1

Henceforth , Our Required Answer is 1 .