Question

If alpha and beta are the zeroes of x2 - 5x + 6, find the value of alpha + beta - 2alphabeta

Answer 1

Given that alpha and beta are the zeroes of polynomial = x² - 5x + 6

here, we've to find the value of alpha + beta - 2(alpha × beta)

so let's find the zeroes of the given polynomial first.

using splitting the middle term method,

➡ x² - 5x + 6 = 0

➡ x² - (3x + 2x) + 6 = 0

➡ x² - 3x - 2x + 6 = 0

➡ x(x - 3) - 2(x - 3) = 0

➡ (x - 3) (x - 2)

➡ x = 3, x = 2

therefore

• alpha = 3

• beta = 2

hence, the value of alpha + beta - 2(alpha × beta)

= 3 + 2 - 2(3 × 2)

= 5 - 2(6)

= 5 - 12

= -7 FINAL ANSWER

Answer 2

Answer: -7

Step-by-step explanation:

We can solve it by taking product of roots and sum of roots respectively using the formula:-

Sum = -b/a

Product = c/a

after finding sum and product put the value of sum and product in the given question which is to be solve.

See the attachment for complete solution:-)