Question

find the zeroes of f(x)=2x²-x-6 and verify the relationship between the zeros and the coefficient ​

Answer 1

Answer:

ans is -3/2 and 2

Step-by-step explanation:

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Answer 2

Answer :

The zeroes of the polynomial are 2 and -3/2

Given :

• Polynomial, f(x)=2x²-x-6

To find :

• Zeroes of the polynomial
• Relationship between zeroes and coefficients

Solution :

Let's find the zeroes of the polynomial by splitting middle term

f(x) = 2x²-x-6

>> 2x²-x-6 = 0

    2x² - 4x + 3x - 6 = 0

    2x(x-2) + 3(x-2) = 0

    (x-2)(2x+3) = 0

         ⇒ (x-2) = 0 : x = 2

         ⇒ 2x+3 = 0 ; x = -3/2

               

The zeroes are 2 and -3/2

Relationship between zeroes and coefficient :

polynomial 2x²-x-6 is of the form ax²+bx+c

      a = 2, b = -1, c = -6

>> Sum of zeroes =  2 + (-3/2)

                             = 2 - 3/2

                             = (4-3)/2

                             = 1/2

                             = -(-1)/2

                             = -b/a = -(x coefficient)/x² coefficient

>> Product of zeroes = 2(-3/2)

                                    = -6/2

                                    = c/a = constant/x² coefficient

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