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If alpha is a root of the equation x^2+2...

If `alpha` is a root of the equation `x^2+2x-1=0,` then prove that `4alpha^2-3alpha` is the other root.

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If a,b,c are in G.P. then the roots of the equation a x^2 + bx + c = 0...

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  2. Let a gt 0, b gt 0 then both roots of the equation ax^(2)+bx+c=0

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  3. If alpha is a root of the equation x^2+2x-1=0, then prove that 4alpha^...

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  4. If alpha, beta are the roots of the equations x^2+px+q=0 then one of t...

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  5. Let a and b be roots of x^2-3x+p=0 and let c and d be the roots of x^...

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  6. If alpha,beta are the nonzero roots of a x^2+b x+c=0a n dalpha^2,beta^...

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  7. If alpha,beta are the roots of the equation ax^2+bx+c=0 and Sn=alpha^n...

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  8. If alpha,beta be the roots of the equation lambda^2(x^2 - x) + 2lambda...

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  9. If a, b are the roots of x^2 + px + 1 = 0 and c, d are the roots of ...

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  10. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

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  11. If alpha,beta are roots of x^2-px+q=0 then find the quadratic equation...

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  12. The coefficient of x in the equation x^2+px+q=0 was wrongly written as...

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  13. In copying a quadratic equation of the form x^2 +px +q=0,a student wro...

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  14. Find p in R for which x^2-px+p+3=0 has one positive and one negative r...

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  15. Find p in R for which x^2-px+p+3=0 has one root>2 and the other root<2...

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  16. For what values of a inR, the quadratic equation (a^2+1)x -(a+l)x+( a^...

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  17. For what values of a, does the equation ax^2 -(a + 1)x + 3 = 0, have r...

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  18. Find the real values of the parameter a such that (2a + 1)x^2-a(x-1) =...

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  19. Find the integral values of a for which the equation x^4-(a^2-5a+6)x^2...

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  20. Find the values of k so that the quadratic equation x^2 + 2(k-1)x + k+...

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