Find the zeroes of the polynomial $p (x) = 2 x^{2} - 5 x - 12$ and verify the relationship between its zeroes and coefficients.

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Solution

find the zeros of polynomial
$p (x) = 2 x^{2} - 5 x - 12$ and verify
the relationship between its zeros and coefficients
We will use side charge method
$2 π^{2} - 5 x - 12 = 0$
it is in form $a x^{2} + b x + c = 0$
$a = 2$
$b = - 5$
$c = - 12$
To find zeroes we will are relation
of coefficients as a formula
$x = \frac{- b \pm \sqrt{6^{2} - 4 a c}}{2 a}$
$= \frac{- (- 5) \pm \sqrt{25 - 4 \times 2 \times (- 12)}}{2 \times 2}$
$= \frac{5 \pm \sqrt{25 + 96}}{4} = \frac{5 \pm 11}{4}$
zeros or $x \frac{16}{4} = 4$ and $\frac{5 - 11}{4} = \frac{- 6}{4} = \frac{- 3}{2}$

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Find the zeroes of the polynomial p(x)=2x2−5x−12 and verify the relationship between its zeroes and coefficients.

Find the zeroes of the polynomial $p (x) = 2 x^{2} - 5 x - 12$ and verify the relationship between its zeroes and coefficients.