हिंदी

If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’ - Algebra

Advertisements
Advertisements

प्रश्न

If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’

योग
Advertisements

उत्तर

3y2 + ky + 12 = 0 

Comparing the above equation with

ax2 + by + c = 0, we get

a = 3, b = k, c = 12

∆ = b2 – 4ac

= (k)2 – 4 × 3 × 12

= k2 – 144

= k2 – (12)2

∆ = (k + 12)(k – 12)    ......[∵ a2 – b2 = (a + b)(a − b)]

Since the roots are real and equal,

∆ = 0

∴ (k + 12)(k – 12) = 0

∴ k + 12 = 0 or k – 12 = 0

∴ k = – 12 or k = 12

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Quadratic Equations - Q.2 (B)

संबंधित प्रश्न

Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.


If x=`1/2`, is a solution of the quadratic equation 3x2+2kx3=0, find the value of k


Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.


Without solving, examine the nature of roots of the equation 2x2 + 2x + 3 = 0


Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.


Determine the nature of the roots of the following quadratic equation:

(b + c)x2 - (a + b + c)x + a = 0


In the following determine the set of values of k for which the given quadratic equation has real roots:

3x2 + 2x + k = 0


Determine the nature of the roots of the following quadratic equation : 

2x2 + x-1=0 


Find the value(s) of k for which the pair of equations
kx 2y = 3
3x + 6y = 10
 has a unique solution.


Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`


Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0


Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.


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


Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.


Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)


State whether the following quadratic equation have two distinct real roots. Justify your answer.

3x2 – 4x + 1 = 0


If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.


If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.


Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.


If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×