Question

19. Find the quadratic polynomial whose zeroes are in the ratio 2:3 and their sum is 15.​

Answer 1

Answer:

x²-15x+6

Step-by-step explanation:

given:- sum of zeroes = 15

-b/a = 15

than, b = -15 and a = 1

and ratio of zeroes =2:3

product of zeroes = c/a

6 = c/a

then, c = 6 and a = 1

hence, the quadratic polynomial will be

x²-15x+6...

Answer 2

Given:-

• Ratio of the zeroes of the quadratic polynomial = 2:3
• Sum of the zeroes = 15

To Find:-

• The quadratic polynomial

Assumption:-

• Let the ratio constant be x
• 1st zero = 2x
• 2nd zero = 3x

Solution:-

As it is given that the sum of the zeroes is 15

Hence,

2x + 3x = 15

=> 5x = 15

=> x = 15/5

=> x = 3

Now,

1st zero = 2x = 2 × 3 = 6

2nd zero = 3x = 3 × 3 = 9

Now,

As the sum of the zeroes is already given,

Let us find out the product of the zeroes.

This

Product of the zeroes = 6 × 9 = 54

So we have

• Sum of zeroes = 15
• Product of zeroes = 54

Wee know,

A quadratic equation is always in the form:-

x² - (sum of the zeroes)x + product of zeroes

Hence,

Putting the values:-

x² - (15)x + 54

=> x² - 15x + 54

Hence, the required quadratic equation is x² - 15x + 54.

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Verification!!!

Let us verify whether the equation we got is correct or not.

We know,

Sum of zeroes = -(Coefficient of x)/(Coefficient of x²)

Hence,

= 15 = -(-15)/1

=> 15 = 15

Also,

Product of zeroes = (Constant Term)/Coefficient of x²)

= 54 = 54/1

=> 54 = 54

Hence, Verified!!!

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