Math, asked by ushasrichinnu58, 6 months ago

check whether 0-1 and ¼ are zeroes of polynomial p(x)=4x²+3x-1

Answers

Answered by snehitha2
2

Correct Question :

Check whether -1 and ¼ are zeroes of polynomial p(x)=4x²+3x-1

Answer :

-1 and ¼ are zeroes of polynomial p(x)=4x²+3x-1

Step-by-step explanation :

Quadratic Polynomials :

       ✯ It is a polynomial of degree 2

       ✯ 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 + 3x - 1

we have to check whether -1 and 1/4 are the zeroes of the given polynomial.

  • substitute x = -1,

p(-1) = 4(-1)² + 3(-1) - 1

       = 4(1) - 3 - 1

       = 4 - 3 - 1

       = 4 - 4

       = 0

Since p(-1) = 0,

∴ -1 is a zero of the polynomial 4x²+3x-1

  • substitute x = 1/4

p(1/4) = 4(1/4)² + 3(1/4) - 1

         = 4(1/16) + 3/4 - 1

         = 1/4 + 3/4 - 1

         = 4/4 - 1

         = 1 - 1

         = 0

Since p(1/4) = 0,

∴ 1/4 is a zero of the polynomial 4x²+3x-1

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