Question

If one root of polynomial 2x^2-3x+p os 3 find the other root and value of p

Answer 1

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2x²-3x+p

root (a)=3

root (b)=?

p=?

f(a)=2x²-3x+p

f(3)=0

0=2(3²)-3(3)+p

0=2(9)-9+p

0=18-9+p

0=9+p

p=-9

f(x)=2x²-3x-9

2x²-6x+3x-9=0

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

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

x=-3/2,3

Answer 2

In the quadratic equation $ax^2+bx+c=0$, the sum pf the roots is $-\frac{b}{a}$ and the product of the roots is $\frac{c}{a}$.

For the equation $2x^2-3x+p=0$,

sum of the roots is

$3+\alpha =\frac{3}{2} ,\alpha =-\frac{3}{2}$

Also product of the roots,

$3(-\frac{3}{2} )=\frac{p}{2} ,p=-9$,

Thus the other root is $-\frac{3}{2}$ and $p=-9$