Question

 If one zero of the polynomial 2 x^2 – 7 x + p is 1/2 , then the value of p and other zeroes respectively is​

Answer 1

$\large\bf\underline{Given:-}$

• p(x) = 2x² - 7x +p
• one zero is given = 1/2

$\large\bf\underline {To \: find:-}$

• Value of p.

$\huge\bf\underline{Solution:-}$

• P(x) = 2x² - 7x +p

• x = 1/2

putting value of x in the given polynomial.

$:\implies\rm\: {2x}^{2} - 7x + p = 0 \\ \\ :\implies\rm\:2 \times { (\frac{1}{2}) }^{2} - 7 \times \frac{1}{2} + p = 0\\ \\ :\implies\rm\cancel2 \times \frac{1}{ \cancel4} - \frac{7}{2} + p = 0\\ \\ :\implies\rm \frac{1}{2} - \frac{7}{2} + p = 0 \\ \\ :\implies\rm\: \frac{1 - 7 + 2p}{2} = 0 \\ \\ :\implies\rm\: - 6 + 2p = 0 \times 2 \\ \\ :\implies\rm\:2p = 6 \\ \\ :\implies\rm\:p = \cancel \dfrac{6}{2} \\ \\ :\implies\bf\:p = 3$

• value of p is 3

$\bf\underline{Verification}$

⠀⠀⠀⠀⠀➝ 2x² - 7x + 3

⠀⠀⠀⠀⠀➝ 2x² - 6x - x +3

⠀⠀⠀⠀⠀➝ 2x(x-3) -1(x -3)

⠀⠀⠀⠀⠀➝ (2x-1)(x-3)

⠀⠀⠀⠀⠀➝ x = 1/2 or x = 3

So we get the zero 1/2 which is given in the question.

Hence verified that value of p is correct.