find the sum and product of roots of the following quadratic equation: 3x²+7x+1=0
Answers
Answer:
alpha + beta = -b/a = -7/3
alphabeta = c/a = 1/3
Sum of the zeroes is -7/3 and product is 1/3
Answer:
If a quadratic equation is given in standard form, we can find the sum and product of the roots using coefficient of x2, x and constant term.
Let us consider the standard form of a quadratic equation,
ax2 + bx + c = 0
(Here a, b and c are real and rational numbers)
Let α and β be the two zeros of the above quadratic equation.
Then the formula to get sum and product of the roots of a quadratic equation is,
Example 1 :
Find the sum and product of roots of the quadratic equation given below.
x2 - 5x + 6 = 0
Solution :
Comparing
x2 - 5x + 6 = 0
and
ax2 + bx + c = 0
we get
a = 1, b = -5 and c = 6
Therefore,
Sum of the roots = -b/a = -(-5)/1 = 5
Product of the roots = c/a = 6/1 = 6
Example 2 :
Find the sum and product of roots of the quadratic equation given below.
x2 - 6 = 0
Solution :
Comparing
x2 - 6 = 0
and
ax2 + bx + c = 0
we get
a = 1, b = 0 and c = -6
Therefore,
Sum of the roots = -b/a = 0/1 = 0
Product of the roots = c/a = -6/1 = -6