2 A quadratic polynomial whose sum of zeroes is 5 and product is 6 will be a) x 2 +5x+6 b) x 2 -5x+6 c) x 2 +5x-6 d) x 2 -5x-6
Answers
Answer: b) x^2 - 5x + 6
Step-by-step explanation:
If p and q are roots of a quadratic equation ax^2 + bx + c=0
Sum of roots = (p + q) = - [(Coefficient of x) / (Coefficient of x^2)]
Product of roots = pq =[ (constant or c) / (Coefficient of x^2)]
The Quadratic equation can be written as
a( x - p)(x - q)=0
a(x^2 -px - qx + pq)=0
a(x^2 -(p+q)x + pq )=0 ---------3
So we can write
p + q=-b/a ------1 and pq=c/a --------2
We have been given value of sum of zeroes or roots as 5 = p+q
Product of zeroes is 6 = pq
Substituting values of p+q and pq in 1 and 2 we get
p+q=5 = -b/a
pq=6 = c/a
So b = - 5a and c = 6a
a=1 as coefficient of x^2 is 1 in all options
Substituting these values in 3 we get
1(x^2 - (5)x + 6)=0
x^2 - 5x + 6=0
Therefore the answer is b) x^2 - 5x + 6