Question

if alpha and beta are the zeroes of the quadratic polynomial p(x)=x2+12x+35 form a quadratic polynomial whose zeros are 2alpha,2 beta​

Answer 1

Solution :

Given : α and ß are the Zeroes of the Quadratic Polynomial x² + 12x + 35 .

So, Sum of Zeroes = - b/a

↪ α + ß = -12/1

↪ α + ß = - 12

Now, Product of Zeroes = c/a

↪ αß = 35 /1

↪ αß = 35


Now, According to the Question !

[ Following are the Zeroes of New Quadratic Polynomial . ]



Sum of Zeroes = 2α + 2ß

Sum of Zeroes = 2 ( α + ß )

Sum of Zeroes = 2 ( -12 )

Sum of Zeroes = -24

Now, We have to Find the product of Zeroes !

Product of Zeroes = 2α × 2ß

Product of Zeros = 2 ( α × ß )

Product of Zeroes = 2 ( 35 )

↪ Product of Zeroes = 70


Now, New Quadratic Polynomial : x² - ( α + ß)x + αß


↪x² - ( α + ß)x + αß

↪ x² - (-24)x + 70

↪ x² + 24x + 70


Hence, Required Quadratic Polynomial is x² + 24x + 70.

Answer 2

___________________________________

Answer :


Sum of Zeroes = - b/a

α + ß = -12/1

α + ß = - 12

Now, Product of Zeroes = c/a

αß = 35


Sum of Zeroes = 2α + 2ß

=> 2 ( -12 ) = -24

Now,

Product of Zeroes = 2α × 2ß


2 ( 35 )

= 70


Hence, General Formula of Quadratic is x² - ( α + ß)x + αß

x² - (-24)x + 70

=> x² + 24x + 70 ( Answer )