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 roots are real and equal in each of the following equation:
(3k+1)x2 + 2(k + 1)x + k = 0
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
2x2 - (3k + 1)x - k + 7 = 0.
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Which of the following equations has no real roots?
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case.
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’.
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
Every quadratic equations has at most two roots.
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
For the equation \( x^{2} + 2x - 9 = 0 \), what conclusion is drawn about its roots since \( b^{2} - 4ac = 40 \)?
