Question

find the zeros of Polynomial is 4x²+5√2x-3 and verify the relationship between zeros and cofficient​

Answer 1

Answer: P[X]=4X²+5✓2X-3

4X²+6✓2X-✓2X-3

2✓2X(✓2X+3) -1(✓2X+3)

(✓2X+3) (2✓2X-1) = 0

(✓2X+3) = 0 OR (2✓2X-1) = 0

=> X = -3/✓2 OR X = 1/2✓2

=> X = -3/✓2 OR X = 1/2✓2

3/✓2 and 1/2✓2 are the two zeroes of the given polynomial.

Let Alpha=-3/✓2 and beta = 1/2✓2

Relationship between the zeroes and coefficient.

Sum of Zeros= (Alpha + Beta) = -3/✓2 + 1/2✓2 = -3×2✓2 + ✓2 = -6✓2+✓2/4 = -5✓2/4 = -( Coefficient of X/Coefficient of X².

And product of zeroes=(-3/✓2 × 1/2✓2) = -3/4 =Constan term/Coefficient of X².

HOPE IT WILL HELP U