Question

If alpha and beta are the zeros of 2x square+5x-10,then find the value of alpha and beta​

Answer 1

p (x ) = 2x^2 + 5x - 10

given : α and β are zeroes of polynomial .

α + β = - b / a = - ( - 5 ) / 2 ...............(i)

α.β = c / a = 7 / 2 ...............(ii)

i think zeroes of the polynomial will be there .

so if zero of the polynomial are assumed to be [ 2α + 3 β ] and [3 α + 2 β ]

Answer 2

We need to recall the quadratic formula for the roots of a quadratic equation.

The roots of the quadratic equation $ax^{2} +bx+c=0$ are:

 $x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Given:

$\alpha ,\beta$  are the roots of the quadratic equation $2x^{2} +5x-10=0$.

From the quadratic formula, we get

$x=\frac{-5\pm\sqrt{5^2-4(2)(-10)} }{2(2)}$

$x=\frac{-5\pm\sqrt{25+80} }{4}$

$x=\frac{-5\pm\sqrt{105} }{4}$

Hence, the values of the roots are $\alpha=\frac{-5+\sqrt{105} }{4}$   and  $\beta =\frac{-5-\sqrt{105} }{4}$ .