Question

if one zero of the quadratic polynomial 2x²+px+4 is 1, then find the value of p.​

Answer 1

Step-by-step explanation:

gave any further questions

AB289

Answer 2

Solution :

$\bigstar$ We have quadratic polynomial 2x² + px + 4 & one zero is given β = 1

As we know that given polynomial compared with ax² + bx + c;

• a = 2
• b = p
• c = 4

Now;

$\underline{\large{\mathcal{SUM\:OF\:THE\:ZEROES\::}}}$

$\mapsto\sf{\alpha +\beta =\dfrac{-b}{a} =\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2} } }\\\\\\\mapsto\sf{\alpha +1=\dfrac{-p}{2} }\\\\\\\mapsto\sf{\alpha =\dfrac{-p}{2} -1.....................(1)}$

$\underline{\large{\mathcal{PRODUCT\:OF\:THE\:ZEROES\::}}}$

$\mapsto\sf{\alpha \beta =\dfrac{c}{a} =\dfrac{Constant\:term}{Coefficient\:of\:x^{2} }}\\\\\\\mapsto\sf{\alpha \times 1=\cancel{\dfrac{4}{2} }}\\\\\\\mapsto\bf{\alpha =2}$

Putting the value of α in equation (1),we get;

$\mapsto\sf{2=\dfrac{-p}{2} -1}\\\\\mapsto\sf{2\times2 =-p-2}\\\\\mapsto\sf{4=-p-2}\\\\\mapsto\sf{-p=4+2}\\\\\mapsto\sf{-p=6}\\\\\mapsto\bf{p=-6}$

Thus;

The value of p will be -6 .