हिंदी

From the Quadratic Equation If the Roots Are 6 and 7. - Algebra Mathematics 1

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

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

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:

2x2 - 3x + 5 = 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.


Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.


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

2(a2 + b2)x2 + 2(a + b)x + 1 = 0


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

x2 - 2(5 + 2k)x + 3(7 + 10k) = 0


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

2x2 − 5x − k = 0


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

2x2 + kx + 2 = 0


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

 x2 -4x + 4=0 


`(2)/x^2 - (5)/x + 2` = 0


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


Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0


Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.


Choose the correct answer from the given four options :

If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are


If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case


If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:


The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, 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 whether the following equation have real roots. If real roots exist, find them.

`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`


Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.


For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×