Question

If Alpha And Beta are zeroes of the polynomial 4x²+3x+7 find the value of (i) alpha² × beta² (ii) 1/alpha + 1/beta
please help​

Answer 1

Answer:

I) alpha² x beta² is equal to 49/16

2) 1/alpha + 1/beta is equal to -3/7

Answer 2

Answer:

alpha² × beta² = (49/16)

(1/alpha) + (1/beta) = (-3/7)

Step-by-step explanation:

4x² + 3x + 7 = 0

ax² + bx + c = 0

where a = 4, b = 3, c = 7

We know that,

The zeroes of the polynomial is Alpha and Beta.

Let alpha be 'a' and beta be 'b' .

Now,

Sum of Zeroes = -b/a

a + b = -(3)/4

a + b = -3/4 ----- 1

Also,

Product of zeroes = c/a

ab = 7/4 ----- 2

Now,

We must find a²b² and (1/a) + (1/b)

Now,

We know that,

a^m × b^m = (a × b)^m

Similarly,

a²b² = (a × b)²

= (ab)²

We know from eq.2

ab = 7/4

Thus,

(ab)² = (7/4)²

a²b² = 49/16

Hence, alpha² × beta² = (49/16)

Now,

(1/a) + (1/b) = (b + a)/ab

(1/a) + (1/b) = (a + b)/ab

We know from eq.1 and eq.2

a + b = (-3)/4

ab = 7/4

Now,

(a + b)/ab = ((-3)/4)/(7/4)

(a + b)/ab = -3/4 ÷ 7/4

(a + b)/ab = -3/4 × 4/7

(a + b)/ab = -3/7

Thus,

(1/alpha) + (1/beta) = (-3/7)

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