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Show f(x)=x^3+px+q=0 has a repeated root...

Show f(x)=`x^3+px+q`=0 has a repeated root if `4p^3+27q^2`=0

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Let p,q be real numbers. If alpha is the root of x^2+3p^2x+5q^2=0 , beta is a root of x^2+9p^2x+15q^2=0 and 0ltalphaltbeta , then the equation x^2+6p^2x+10q^2=0 has a root gamma that always satisfies.

If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of x^2+px+r=0, p+rphi0 ,then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta)) is equal to

Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the roots of x^2-4x+q=0 . If alpha,beta,gamma are in GP , then the integer values of p and q respectively are:

If the roots of the equation x^2-px+q=0 be alpha,beta and the roots of the equation x^2-ax+b=0 be alpha,1/beta then prove that, bq(a-p)^2=(q-b)^2 .

If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^(2) – 12x + q = 0 , where a,b,c,d form a G.P Prove that (q+q):(q-p) = 17 : 15

Given that a,c are the roots of the equation px^2-3x+2=0 and b,d are the roots of the equation qx^2-4x+2=0 , find the values of p and q such that 1/a,1/b,1/c and 1/d are in A.P.

If the difference of the roots of the equation x^2-px+q=0 is 1, then show that p^2+4q^2= (1+2q)^2 .

IF alpha and beta be the roots of the equation x^2+px+q=0 show that alpha/beta is a root of the equation qx^2-(p^2-2q)x+q=0 .

If one root of the equation x^2+px+12=0 is 4, while the equation x^2+px+q =0 has equal roots, then the value of q is

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. Let P(x)equiv ((x-a)(x-b))/((c-a)(c-b)).c^2+((x-b)(x-c))/((a-b)(a-c))....

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  2. Solve the equation (x^2-6x)^2=81+2(x-3)^2

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  3. Show f(x)=x^3+px+q=0 has a repeated root if 4p^3+27q^2=0

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  4. Show x^5-2x^2+7=0 has atleast two imaginary roots.

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  5. Solution set of x satisfying abs(x/(x-1))+absx=x^2/abs(x-1) is

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  6. Solve the equation abs(x-abs(4-x))-2x=4

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  7. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  8. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  9. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  10. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  11. Find two negative integers whose difference is 3 and sum of their squa...

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  12. If alpha and beta are roots of ax^2+bx+c=0 then prove that (alpha/bet...

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  13. If (p^2+2)x^2+2p^2x+(P^2-4)=0 has root of opposite sign,then find the ...

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  14. Find the condition such that the quadratic equations ax^2+bx+c=0 and x...

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  15. If (x-1) is the factors fo polynomial x^3-px+q, then prove that p-q=1

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  16. Two roots of the equation,x^3+qx^2+11x-p=0 are 2 and 3, find (p-q)

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  17. Find the values of K for which the inequality (x-3k)(x-k-3)lt0 is sati...

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  18. Let alpha and beta be the roots of the equation ax^2+2bx+c=0 and alpha...

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  19. If sin theta,costheta are the roots of the equation ax^2+bx+c=0 then f...

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  20. If the roots alpha and beta of the quadratic equation ax^2+bx+c=0 are ...

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