Question

The sum and the product of the equation x² + px + q = 0 are 4 and -3 respectively.The values of p and q are respectively
(a) 4 , 3
(b) -4 , -3
(c) -4 , 3
(d) 4 , -3​

Answer 1

Solution :

We have quadratic polynomial p(x) = x² + px + q = 0;

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

• a = 1
• b = p
• c = q

Now;

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

$\mapsto\sf{\alpha +\beta = \dfrac{-b}{a} =\bigg\lgroup \dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}} }\bigg\rgroup }\\\\\\\mapsto\sf{4 = \dfrac{-p}{1}} \\\\\\\mapsto\sf{-p=4}\\\\\mapsto\bf{p=-4}$

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

$\mapsto\sf{\alpha \times \beta = \dfrac{c}{a} =\bigg\lgroup \dfrac{Constant\:term}{Coefficient\:of\:x^{2}} }\bigg\rgroup }\\\\\\\mapsto\sf{-3= \dfrac{q}{1}} \\\\\\\mapsto\sf{-3=q}\\\\\mapsto\bf{q=-3}$

Thus;

The value of p & q are -4 & -3 .

Option (b)

Answer 2

Answer:

b) - 4, - 3

Step-by-step explanation:

Given

Sum : 4

Product : - 3

Sum of zeroes = - b /a

Product of zeroes = c/a

- 4 = p/1

- 3 = q /1

So, the answer is :-

p= - 4

q =-3