Question

2x^2-3+5x find the zreoes of the ploynomial​

Answer 1

Answer:

Let f(x) = 2x^2 - 3 + 5x.

Zero of the polynomial is where f(x) = 0

= > 2x^2 + 5x - 3 = 0

= > 2x^2 - x + 6x - 3 = 0

= > x(2x - 1) + 3(2x - 1) = 0

= > (x + 3)(2x - 1) = 0

= > x = -3, 1/2.

So, α = -3, β = 1/2 are the zeroes of the polynomial.

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Comparing 2x^2 + 5x - 3 with ax^2 + bx + c,

We get a = 2, b = 5, c = -3.

Verification:

(i)

Sum of zeroes = -b/a

α + β = -b/a

-3 + 1/2 = -5/2

-6 + 1/2 = -5/2

-5/2 = -5/2

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(ii) Product of zeroes = c/a

αβ = c/a  

-3 * (1/2) = -3/2  

-3/2 = -3/2.

Hence if it proved.

Hope this helps!