Question

Find zeroes of the polynomial 3x 2 - 10x - 8 and verify the relation between zeroes and coefficients.

Answer 1

3x^2-10x-8=0
3x^2-10x=0+8
3x^2-10x=8
x(3x-10)=8
zeroes of the polynomial are 0,-1 and 1

Answer 2

Answer: The zeroes of the equation are 4 and -2/3

Step-by-step explanation:

3x² - 10x - 8 = 0

3x² - 12x + 2x - 8 = 0

3x( x - 4) + 2(x - 4 ) = 0

(3x + 2) ( x - 4 ) = 0

3x + 2 = 0  ,  x - 4 = 0

x = -2/3 , 4

Sum of roots =  $\frac{-2}{3} + 4 =$  $\frac{10}{3}$

Product of roots = $\frac{-2}{3} * 4 = \frac{-8}{3}$

Standard form of quadratic equation ⇒ ax² + bx + c = 0

In the given quadratic equation , a = 3 , b = -10 and c = -8  

Sum of roots = $\frac{-b}{a}$  = $\frac{10}{3}$

Product of roots = $\frac{c}{a}$  = $\frac{-8}{3}$

We get the same result of sum and product of roots from solving the equation and by relating zeroes and coefficients.

The relation between zeroes and coefficients is verified.

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