Advertisements
Advertisements
प्रश्न
From the quadratic equation if the roots are 6 and 7.
उत्तर
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
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation 2x2 + 2x + 3 = 0
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
The 4th term of an A.P. is 22 and the 15th term is 66. Find the first terns and the common
difference. Hence find the sum of the series to 8 terms.
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
Solve the following quadratic equation using formula method only
`3"x"^2 + 2 sqrt 5x - 5 = 0 `
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots are:
Every quadratic equation has exactly one root.
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 1)(x – 2) + x = 0
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
