Question

if one root of the quadratic polynomial 2 x square - 3 x + P is 3 find the other route also find the value of p​

Answer 1

Given Quadratic Polynomial is

$\sf 2 {x}^{2} - 3x + p$

As one Root is 2

So,

$</p><p>\begin{gathered} \sf2(2 {)}^{2} - 3(2) + p = 0 \\ \\ \implies \sf8 - 6 + p = 0 \\ \\ \implies \sf \bold{\boxed{ \boxed{p = - 2}}}\end{gathered}$

So,

Given Quadratic Polynomial is:-)

$\sf2 {x}^{2} - 3x - 2$

Let Second Root be k.

As we know that

$\begin{gathered} \sf SUM \: OF \: ROOTS = \frac{3}{2} \\ \\ \sf 2 + k = \frac{3}{2} \\ \\ \sf \boxed{ \boxed{ k = \frac{ - 1}{2} }}\end{gathered}$

Which is the second root.

Answer 2

1 is the root of the given quadratic equation. Thus,

(1)2+p(1)+3=0

p+4=0

p=−4

Thus, the equation becomes x2−4x+3=0

x2−x−3x+3=0

x(x−1)−3(x−1)=0

(x−1)(x−3)=0

x=1,3

Hence, the other root of the equation is 3.