Advertisements
Advertisements
Question
From the quadratic equation if the roots are 6 and 7.
Advertisements
Solution
Let α = 6 and β = 7
Sum of roots = α + β
= 6 + 7
α + β = 13
Products of the root = α × β
= 6 × 7
= 42
The quadratic equation is given by ,
`"x"^2 - (α + "β")x + "αβ" = 0`
`"x"^2 - 13"x" + 42 = 0`
APPEARS IN
RELATED QUESTIONS
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x2 + 2(k – 4) x + 4 = 0
Choose the correct answer from the given four options :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Solve for x: 9x2 – 6px + (p2 – q2) = 0
The roots of quadratic equation x2 – 1 = 0 are ______.
