Question

The sum and product of the zeroes of a quadratic polynomial P(x)=ax^ 2+bx+c are -3 and 2 respectively.show
that b+c = 5a​

Answer 1

Answer:

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Answer 2

Note:

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

★ In order to find the zeros of the polynomial , equate it to zero.

★ A quadratic polynomial can have atmost two zeros.

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

• Sum of zeros , (A+B) = -b/a

• Product of zeros , (A•B) = c/a

Solution:

The given quadratic polynomial is :

p(x) = ax² + bx + c .

Now,

=> Sum of zeros = -3 { given }

=> -b/a = -3

=> -b = -3a

=> b = 3a ---------(1)

Also,

=> Product of zeros = 2 { given }

=> c/a = 2

=> c = 2a ------------(2)

Now,

Adding eq-(1) and (2) , we have ;

=> b + c = 3a + 2a

=> b + c = 5a

Hence proved .