Question

the sum and product of the roots of 2x^2-5x+4 are in the ratio​

Answer 1

Answer:

5:4

Step-by-step explanation:

sum of roots = -b/a = 5/2

product of roots = c/a = 4/2

sum:product = 5:4

Answer 2

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Formula: We consider a polynomial

f(x) = ax² + bx+c

If p and q be the zeros of f(x), then

p+q = -b/a

pq = c/a

Solution: The given polynomial is

f(x) = 2x² -5x +4

Let p and q are the zeros of f(x). Then by the relation between zeors and coefficients, we get

p+q=-(-5/2) = 5/2

pq = 4/2 = 2

Thus the ratio of the sum and the product of the zeros is

= (p+q): pq

= 5/2 : 2

= 5:4