Question

If a, ß are the zeros of the polynomial p(x) = 2x2 + 5x + 2, then the value of
a” + ß2 +aß is
(a) 25. (b) 26. (c) 21/4. (d) 25/4​

Answer 1

Answer:

Option (C) 21/4

a² + b² + ab = 21/4

Step-by-step explanation:

I believe your Question was,

"If a, b are the zeros of the polynomial p(x) = 2x2 + 5x + 2, then the value of

a² + ß² + ab is

(a) 25. (b) 26. (c) 21/4. (d) 25/4"

Now,

Let 'a' and 'b' be the zeroes of p(x) = 2x² + 5x + 2

2x² + 5x + 2 = 0

ax² + bx + c = 0

where a = 2, b = 5 and c = 2

We know that,

Sum of zeroes = -b/a

a + b = -(5)/2

a + b = -5/2

Also,

Product of zeroes = c/a

a × b = 2/2

ab = 1

Now,

a² + b² + ab

We know that,

(a + b)² = a² + 2ab + b²

Now,

From a² + 2ab + b² to get a² + ab + b² we must subtract (ab)

thus,

a² + ab + b² = (a + b)² - ab

Now,

a + b = -5/2

ab = 1

Thus,

(a + b)² - ab = (-5/2)² - 1

= 25/4 - 1

= 25/4 - 4/4

= 21/4

Hence, a² + b² + ab = 21/4

Hope it helped and you understood it........All the best