Question

If alpha and beta are zeroes of 4xsquare - x-4. find the quadratic polynomial whose zeroes are 1/3alpha and 1/3beta​

Answer 1

Given:

• a and b are zeroes of 4x² - x -4 .

To find :

• The quadratic polynomial whose zeroes are 1/3a. and 1/3b .

Solution :

•p(x)= 4x² - x - 4 .

Compare with ax² + bx + c we get ,

•a = 4 , b = -1 and c = -4

• Sum of Zeroes ( a + b ) = -b/a = 1/4

• product of zeroes ( ab ) = c/a = -4/4= -1

Now, zeroes are 1/3a and 1/3b

• sum of the zeroes = 1/3(a+b/ab) = 1/3 (1/4/-1)= -1/12

• Product of Zeroes = 1/3a×1/3b = 1/9ab = -1/ 9

Quadratic equations

= x² - (sum of the zeroes)x + product of zeroes = 0

=> x² +1/12 x -1/9 = 0

=> 36x² + 3x - 4 = 0

Hence , the equation is 36x² + 3x - 4 .

Answer 2

Step-by-step explanation:

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