Question

find the zeroes of the polynomial 4x2+5√2x-3 and verify the relations between the zeroes and the coefficients of the polynomial

Answer 1

the sum of zeroes = -b/a= -5√2/4
the product of zeroes= c/a= -3/4
the zeroes are,
4x^2+5√2x-3
4x^2+(2√2+3√2)x-3
4x^2+2√2x+3√2x-3

Answer 2

Step-by-step explanation: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

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

Let Alpha = -3/✓2 and beta = 1/2✓2 hope this helps:)

Relationship between the zeros 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 zeros = (-3/✓2 × 1/2✓2) = -3/4 = Constant term/Coefficient of X².