हिंदी

From the Quadratic Equation If the Roots Are 6 and 7. - Algebra

Advertisements
Advertisements

प्रश्न

From the quadratic equation if the roots are 6 and 7.

योग

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`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2013-2014 (October)

APPEARS IN

संबंधित प्रश्न

If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.


Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.


Find the values of k for which the roots are real and equal in each of the following equation:

`kx^2-2sqrt5x+4=0`


Find the values of k for which the roots are real and equal in each of the following equation:

(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0


Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.


Solve the following quadratic equation using formula method only :

16x2 = 24x + 1 


Solve the following quadratic equation using formula method only :

`2x + 5 sqrt 3x +6= 0 `


Solve the following quadratic equation using formula method only 

4x2 + 12x + 9 = 0 


Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.

x2 + 2(m – 1)x + (m + 5) = 0


Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.


Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.


In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1


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


If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.


Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0


Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.


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

`(x - sqrt(2))^2 - 2(x + 1) = 0`


Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.


The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×