Question

Find a quadratic polynomial, whose zeroes are 3 and -4​.
Find a quadratic polynomial, whose zeroes are -3 and 4.
Find a quadratic polynomial, whose zeroes are -3 and -4​.
Find a quadratic polynomial, whose zeroes are 3 and 4.
(PLEASE DO NOT SPAM/DO YOUR BEST, NEED QUALITY ANSWERS FROM QUALITY USERS)

Answer 1

Given :-

1. Zeroes are 3 and -4
2. Zeroes are -3 and 4
3. Zeroes are -3 and -4
4. Zeroes are 3 and 4

To find : Quadratic polynomial in case

Solution :

Every quadratic polynomial is of the form,

• x² - (sum of zeroes) x + Product of zeroes

So we will find sum and product of zeroes in each case and will substitute the values to get the required polynomial.

______________________

1.) Zeroes are 3 and -4

• Sum of zeroes = 3 - 4 = -1
• Product of zeroes = 3 × (-4) = -12

So the required polynomial is :-

=> x² - (-1) x + (-12)

=> x² + x - 12

______________________

2.) Zeroes are -3 and 4

• Sum of zeroes = -3 + 4 = 1
• Product of zeroes = -3 × 4 = -12

So the required polynomial is :-

=> x² - x + (-12)

=> x² - x - 12

______________________

3.) Zeroes are -3 and -4

• Sum of zeroes = -3 - 4 = -7
• Product of zeroes = -3 × (-4 ) = 12

So the required polynomial is :-

=> x² - ( -7 ) x + 12

=> x² + 7x + 12

______________________

4.) Zeroes are 3 and 4

• Sum of zeroes = 3 + 4 = 7
• Product of zeroes = 3 × 4 = 12

So the required polynomial is :-

=> x² - 7 x + 12

______________________

So the required answers are :-

• x² + x - 12
• x² - x - 12
• x² + 7x + 12
• x² - 7x + 12

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