Advertisements
Advertisements
प्रश्न
Form the quadratic equation if its roots are –3 and 4.
Advertisements
उत्तर
Given that
α = -3, β = 4
∴ α + β = (-3) + 4 = 1
α.β = -3 x 4 = -12
∴ The quadratic equation which roots are α and β is
x2 - (α+β)x + αβ = 0
∴ x2 - x - 12 = 0
APPEARS IN
संबंधित प्रश्न
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
For what value of k, (4 – k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2 - 2sqrt(ac)x + b = 0` are simultaneously real, then prove that b2 = ac.
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and –ax2 + bx + c = 0 has real roots.
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
When the discriminant satisfies \( D > 0 \), what is the nature of the roots of the quadratic equation?
What is the nature of the roots when the discriminant is negative, i.e. \( D < 0 \)?
