Home
Class 10
MATHS
If alpha and beta are the roots of th...

If `alpha ` and `beta ` are the roots of the quadratic equation `x^(2) - 4x - 6 = 0 ` , find the values of `alpha^(2) + beta^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
`alpha^(2) + beta^(2) = 28`
`x^(2) - 4x - 6 = 0 `
Here, `a= 1, b = - 4, c = - 6 `
`alpha + beta = ( - b)/( a) = ( - ( - 4))/( 1)= 4 ` ....(1)
`alpha beta = ( c )/( a ) = ( -6)/( 1) = - 6 ` ....(2)
`alpha^(2) + beta^(2) = ( alpha + beta)^(2) - 2alpha beta ` .....(identity )
`= ( 4)^(2) - 2( - 6)` ...[From (1) and (2) ]
` = 16 + 12 = 28`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise ASSIGNMENT 2.1|8 Videos

  • QUADRATIC EQUATIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise ASSIGNMENT 2.2|5 Videos

  • QUADRATIC EQUATIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise 2.3 (2 MARKS EACH)|7 Videos

  • QUADRATIC EQUATION

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise CHALLENGIN QUESTIONS|2 Videos

  • SIMILARITY

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise SUBJECTIVE TYPE|20 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of the quadratic equation x^(2) - 2x - 7 = 0 , find the value of alpha^(2) + beta ^(2) .

If alphaandbeta are the roots of the quadratic equation x^(2)-4x-6=0 , find the vlaues of alpha^(3)+beta^(3)

If alpha , beta roots of the equations x^(2) - 5x + 6 = 0 , find the value of alpha^(2) - beta^(2) .

If alpha " and " beta are the roots of the quadratic equation x^2 -5x +6 =0 then find alpha^2 + beta^2

If alpha and beta are the roots of the quadratic equation x^(2)-6x+1=0, then the value of (alpha^(2))/(beta^(2))+(beta^(2))/(alpha^(2)) is

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 , then minimum value of alpha^(2)+beta^(2) is

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 ,then minimum value of alpha^(2)+beta^(2) is