Question

16)Find a quadratic polynomial with the given numbers as the sum and product of its

zeros respectively 4 and 2.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\maltese$Given :-

• Sum of zeros of a Quadratic polynomial is 4
• Product of zeros of a Quadratic polynomial is 2

$\maltese$To find:-

• Quadratic polynomial

$\maltese$SOLUTION : -

The required quadratic equation whose sum of roots is $\alpha+\beta$ and product of roots is $\alpha\beta$ is

${\boxed{x^2-(\alpha+\beta)x + \alpha \beta }}$

So,

According to the Question ,

$Sum\:of\: zeros (\alpha+\beta) = 4$

$Product\:of\: zeros (\alpha\beta)= 2$

Required Quadratic polynomial is

$x^2- (\alpha+\beta)x+\alpha\beta$

$x^2- (4)x+ 2$

$x^2-4x+2$

So, the required Quadratic polynomial is x^2-4x+2

Verification:-

So, we got the polynomial since , their sum of zeros should be 4 and product of zeros should be 2

$x^2-4x+2$

Comparing with general form of Quadratic equation ax² + bx + c

• a= 1
• b = -4
• c = 2

As we know product of zeros is c/a

Product of zeros = 2

2/1 = 2

2 = 2

Verifed !

As we know sum of zeros is -b/a

-(-4)/1 = 4

4 = 4

Verified!