Question

If a and b are the polynomial 2x² - 5x + 8 then find the valve of a² + b²

Answer 1

Answer:

a² + b² = -7/8. (The roots are imaginary).

Step-by-step explanation:

Given, a,b are roots of the polynomial 2x² - 5x + 8 = 0.

Now a+ b = 5/2 and ab = 8/2 = 4.

Consider (a+b)² it is equal to a² + b² + 2ab

i.e (5/2)² = a² + b² + 2(4)

a² + b² = 25/4 -8

a² + b² = 25-32/8

a² + b² = - 7/8.

Now if you square a real number it is always positive, and adding two positive numbers always fetches a positive number.

But in above result we can see that adding two positive numbers gave us negative value.

So the roots should complex(a + ib) with non-zero imaginary part.

Answer 2

Answer:

$\frac{-7}{4}$

Step-by-step explanation:

hey, here"s your solution

The given polynomial =  2x²-5x+8

The value required is for a²+b²

we know , sum of zeros of p(x)= α+β = -b/a

                                                  = -(-5)/2= $\frac{5}{2}$

Now, product of zeros of p(x) = αβ = c/a

                                                  = 8/2= 4

now, solving α²+β²

∴ α²+β²= (α+β)²-2αβ

putting the value of α+β and αβ in the above equation...

∴ (α+β)²-2αβ= ($\frac{5}{2}$ )²-2×4

                    = $\frac{25}{4\\}$-8

                    =$\frac{25-32}{4}$

                    = $\frac{-7}{4}$   ANSWER......