The sum and product of the zeros of 2 x square- 5 x + 4 are in which ratio
5 is to 2
5 is to 4
10:4
None of these
Answers
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 .... (1)
pq = 4/2 = 2 ..... (2)
Thus the ratio of the sum and the product of the zeros is
= (p + q) : pq
= 5/2 : 2
= 5 : 4
Therefore option (b) is correct.
Answer:
The sum and product of the zeros of 2 x square- 5 x + 4 are the ratio 5 : 4
Step-by-step explanation:
Let's write the equation below.
2x² - 5x + 4 = 0
The sum of the roots of the quadratic equation is given by:
= -b/a
= 5/2 = 2.5
The product of the roots is = 4/2= 2
Therefore, the ratio of the sum and product of the zeroes of the quadratic equation is:
Sum : Product
= 2.5/2
= 25/20
= 5 : 4