Question

If m and n are two numbers such that m +n = 3 and m-n = 19, then what is the quadratic polynomial whose zeroes are m and n?

a)x²-3x+19. b)x²+3x-88
c)x²+3x-19. d) x²-3x-88​

Answer 1

In the above Question , the following information is given -

m and n are two numbers such that m +n = 3 and m-n = 19.

To find -

What is the quadratic polynomial whose zeroes are m and n?

Options -

a)x²-3x+19.

b)x²+3x-88

c)x²+3x-19.

d) x²-3x-88

Solution -

Here ,

m and n are two numbers such that m +n = 3 and m-n = 19.

So ,

We are given the following two equations In terms of m and n ..

m + n = 3 ......... { 1 }

m - n = 19 ......... { 2 }

Now , add the following equations -

=> 2 m = 22

=> m = 11

=> n = - 8 .

Thus , the two zeroes or the required polynomial are 11 and -8 respectively .

Sum of Zeroes -

=> 11 - 8

=> 3

Product of Zeroes -

=>11 × -8

=> -88 .

Now , a Polynomial can be written as -

x² - ( Sum of Zeroes ) x + ( Product of Zeroes )

=> x² - 3x - 88 .

Thus , the required Polynomial is x² - 3x - 88 .

Hence , Option D is the correct Answer ..

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Answer 2

Given m & n are zeroes of the polynomial . Such that ,

m + n = 3 ... (1) & m - n = 19 ... (2)

Now solve (1) & (2) , i.e., (1) + (2) ,

⇒ ( m+n ) + ( m-n ) = 3+19

⇒ 2m = 22

⇒ m = 11

sub. m = 11  , in (1) , we get ,

⇒ n = 3 - 11

⇒ n = - 8

So two zeroes of the polynomial are 11 & -8 respectively.

There are many methods to find the quadratic polynomial .

Here I will use simple method to find quadratic polynomial.

⇒ ( x + 8 ) ( x - 11 )

⇒ x ( x + 8 ) - 11 ( x + 8 )

⇒ x² + 8x - 11x - 88

⇒ x² - 3x - 88

So the option (d) is correct .