Question

Find a quadratic polynomial the sum of zeroes is30and one zero is 5

Answer 1

Answer:

x² - 30x + 125

Note:

• The general form of a quadratic polynomial is given as ; ax² + bx + c .

• Zeros of a polynomial are the possible values of unknown (variable) for which the polynomial becomes zero .

• In order to find the zeros of a polynomial, equte it to zero.

• A quadratic polynomial has atmost two zero.

• If A and B are the zeros of s quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , (A•B) = c/a

• If A and B are the zeros of any quadratic polynomial, then it is given as ;

x² - (A+B)x + A•B .

Solution:

Here,

It is given that , the sum of required quadratic polynomial is 30 and one of its zero is 5 .

Now,

Let A and B be the zeros of the required quadratic polynomial .

Thus,

According to the question , we have ;

A + B = 30 ------(1)

A = 5 -------(2)

Now,

From eq-(1) and (2) , we have ;

=> A + B = 30

=> 5 + B = 30

=> B = 30 - 5

=> B = 25

Now,

The product of zeros of the required quadratic polynomial will be ;

A•B = 5•25 = 125

Now,

The required quadratic polynomial will be given as : x² - (A+B)x + A•B

ie ; x² - 30x + 125

Hence,

The required quadratic polynomial is :

x² - 30x + 125 .

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

Sum of zeroes of the quadratic polynomial is 30 and one zero is 5.

To Find:

We need to find the quadratic polynomial.

Solution:

Let α and β be the zeroes of the polynomial.

It is given that α = 5 and α + β = 30

So β = 30 - 5

=> β = 25

Now, product of zeroes of the polynomial is αβ = 5 × 25

= 125

Polynomial is:

[x²- (α + β)x + αβ]

= x² - 30x + 125

Therefore the required polynomial is

Therefore the required polynomial is x² - 30x + 125.