8If one zero of the quadraticpolynomial 2x^2-3x+p is 3,find theother z

1.	8If one zero of the quadraticpolynomial 2x^2-3x+p is 3,find theother zero,find the value of pA.3/2,-9B.-3/2,-9C.3/2,9D.-3/2,9
Answer» Solution : $\bf{\red{\underline{\bf{Given\::}}}}$ If one zero of the quadratic POLYNOMIAL 2x² - 3x + p is 3. $\bf{\red{\underline{\bf{To\:find\::}}}}$ The other zero and the VALUE of p. $\bf{\red{\underline{\bf{Explanation\::}}}}$ We have f(X) = 2x² - 3x + p Zero of the polynomial f(x) = 0 3 is the zero of f(x) So; $\longrightarrow\sf{2(3)^{2} -3(3)+p=0}\\\\\longrightarrow\sf{2\times 9-9+p=0}\\\\\longrightarrow\sf{18-9+p=0}\\\\\longrightarrow\sf{9+p=0}\\\\\longrightarrow\sf{p=0-9}\\\\\longrightarrow\sf{\orange{p=-9}}$ Now; $\longrightarrow\sf{f(x)=2x^{2} -3x-9=0}\\\\\longrightarrow\sf{2x^{2} -6x+3x-9=0}\\\\\longrightarrow\sf{2x(x-3)+3(x-3)=0}\\\\\longrightarrow\sf{(x-3)(2x+3)=0}\\\\\longrightarrow\sf{x-3=0\:\:\:Or\:\:\:2x+3=0}\\\\\longrightarrow\sf{x=3\:\:\:Or\:\:\:2x=-3}\\\\\longrightarrow\sf{\orange{x=3\:\:\:Or\:\:\:x=\dfrac{-3}{2} }}$ Thus; $\underbrace{\bf{The\:other\:zero\:will\:be\:\:\boxed{\sf{\frac{-3}{2} }}}}}\\\underbrace{\bf{The\:value \:of\:p\:wil\:be\:\:\boxed{\sf{-9 }}}}}\\$

8If one zero of the quadraticpolynomial 2x^2-3x+p is 3,find theother zero,find the value of pA.3/2,-9B.-3/2,-9C.3/2,9D.-3/2,9

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Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

If one zero of the quadratic POLYNOMIAL 2x² - 3x + p is 3.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The other zero and the VALUE of p.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We have f(X) = 2x² - 3x + p

Zero of the polynomial f(x) = 0

3 is the zero of f(x)

So;

$\longrightarrow\sf{2(3)^{2} -3(3)+p=0}\\\\\longrightarrow\sf{2\times 9-9+p=0}\\\\\longrightarrow\sf{18-9+p=0}\\\\\longrightarrow\sf{9+p=0}\\\\\longrightarrow\sf{p=0-9}\\\\\longrightarrow\sf{\orange{p=-9}}$

Now;

$\longrightarrow\sf{f(x)=2x^{2} -3x-9=0}\\\\\longrightarrow\sf{2x^{2} -6x+3x-9=0}\\\\\longrightarrow\sf{2x(x-3)+3(x-3)=0}\\\\\longrightarrow\sf{(x-3)(2x+3)=0}\\\\\longrightarrow\sf{x-3=0\:\:\:Or\:\:\:2x+3=0}\\\\\longrightarrow\sf{x=3\:\:\:Or\:\:\:2x=-3}\\\\\longrightarrow\sf{\orange{x=3\:\:\:Or\:\:\:x=\dfrac{-3}{2} }}$

Thus;

$\underbrace{\bf{The\:other\:zero\:will\:be\:\:\boxed{\sf{\frac{-3}{2} }}}}}\\\underbrace{\bf{The\:value \:of\:p\:wil\:be\:\:\boxed{\sf{-9 }}}}}\\$