Question

If a and ß are the zeroes of the polynomial p(x) = 3x2-4x-7 then form a

quadratic polynomial whose zeroes are and B.​

Answer 1

Given Equation:

p(x) = 3x² - 4x - 7 = 0

Zeroes of the equation:

a, ß

Solution:

Let the given equation be = ax² + bx + c = 0

Then:

• Sum of zeroes = -b/a
• Product of zeroes = c/a

Here, when equation is given as 3x² - 4x - 7 = 0

Then:

• Sum of zeroes = 4/3 = a + ß ___*1*
• Product of zeroes = -7/3 = aß ______*2*

We need to find equation with the zeroes: 1/a and 1/ß

Here:

• Sum of zeroes = 1/a + 1/ß

Take LCM:

=> (a + ß)/aß

From *1* and *2*:

=> (4/3)/(7/3)

=> 4/7

Thus, the sum of the zeroes of the new equation is 4/7.

4/7 = sum of zeroes = -b/a

=> -b/a = 4/7 ___(1)

• Product of zeroes = 1/a × 1/ß

=> 1/aß

From *2*:

=> 1/(-7/3)

=> -3/7

Thus, the product of zeroes of the new equation is -3/7.

-3/7 = product of zeroes = c/a

=> c/a = -3/7 ____(2)

Formula for finding equation:

Polynomial = x² - (sum of zeroes)x + (product of zeroes)

Put (1) and (2):

Polynomial = x² - (4/7)x + (-3/7) = 0

Multiple whole equation by 7, to make them whole numbers:

Polynomial = 7x² - 4x - 3 = 0

Thus, your answer is:

7x² - 4x - 3