Question

if one root. of quadratic equation 2x2-3x+p=0 is 3 find the value of p

Answer 1

one root of
$2 {x}^{2} - 3x + p = 0$
is 3
means that if 3 is substituted in the place of x, the equation will be valid
$2 \times {3}^{2} - 3 \times 3 + p = 0$
which simplifies to
$18 - 9 + p = 0 \\ 9 = - p \\ p = - 9$
And that's your answer!

Answer 2

Answer:

Let f(x) = 2x2 - 3x + p

If f(a) = 0, then it is said that a is a zero of f(x).

Given, 3 is a zero of f(x).

f(3) = 0

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

18 - 9 + p = 0

p = -9

f(x) = 2x2 - 3x - 9

= 2x2 - 6x + 3x - 9

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

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

Thus, the other zero of f(x) is $\frac{-3}{2}$.