Question

If alpha and beta are roots of quadratic polynomial x^2-(k-6)x+2k+1 and alpha and beta =alpha × beta . Find the value of k

Answer 1

Solution :

Given Statement : If alpha and beta are roots of quadratic polynomial x²-(k-6)x+( 2k+1)

So, Sum of Zeroes = -b/a

⇒ a + ß = k - 6

Now, Product of Zeroes = c/a

⇒ a × ß = (2k+1)

Now, According to the Question's Statement!

Statement : Sum of Zeroes of Polynomial is Equal to the Product of Zeroes of Polynomial i.e a + ß = a × ß

⇒ a + ß = a × ß

⇒ k - 6 = 2k + 1

⇒ k - 6 = 2k + 1

⇒ k - 2k = 1 + 6

⇒ - k = 7

Therefore, Required Value of k is -7.

Answer 2

Answer:

Given Statement : If alpha and beta are roots of quadratic polynomial x²-(k-6)x+( 2k+1)

So, Sum of Zeroes = -b/a

⇒ a + ß = k - 6

Now, Product of Zeroes = c/a

⇒ a × ß = (2k+1)

Now, According to the Question's Statement!

Statement : Sum of Zeroes of Polynomial is Equal to the Product of Zeroes of Polynomial i.e a + ß = a × ß

⇒ a + ß = a × ß

⇒ k - 6 = 2k + 1

⇒ k - 6 = 2k + 1

⇒ k - 2k = 1 + 6

⇒ - k = 7

Therefore, Required Value of k is -7.

Step-by-step explanation: