Question

If the zeroes of the polynomial p(x) = -4x²+6x+p are opposite of reciprocal of the other, then p=

Answer 1

Answer :

p = -4

Step-by-step explanation :

➤ Quadratic Polynomials :

 ✯ It is a polynomial of degree

 ✯ General form :

           ax² + bx + c  = 0

           $\boxed{\bf x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }$

                                                                    

 ✯ Determinant, D = b² - 4ac

 ✯ Based on the value of Determinant, we can define the nature of roots.

         D > 0 ; real and unequal roots

         D = 0 ; real and equal roots

         D < 0 ; no real roots i.e., imaginary

 ✯ Relationship between zeroes and coefficients :

           ✩ Sum of zeroes = -b/a

           ✩ Product of zeroes = c/a

_______________________________

Given,

• Polynomial, p(x) = -4x² + 6x + p

             It is of the form ax² + bx + c

             a = -4, b = 6, c = p

• Zeroes are reciprocal to each other.

Let the zeroes be α and 1/α

we know,

  Product of zeroes = c/a

          α × (1/α) = p/-4

              1 = p/-4

              p = -4

∴ The value of p is -4