The roots of the equation 2x^2-3x+5=0 are alpha and beta and the roots of the equation px^2+x+q=0 are alpha-1 and beta-1. Find the value of p and q

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2x^2 - 3x + 5 = 0 has roots alpha, beta alpha + beta = -(-3)/2 => alpha + beta = 3/2 (alpha)(beta) = 5/2 px^2 + x + q = 0 has roo...

If roots of equation (h^2-a^2)x^2-2hkx+(k^2-b^2)=0 are real and equal, prove that h^2/a^2 + k^2/b^2 = 1

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We have the equation (h^2-a^2)x^2-2hkx+(k^2-b^2)=0 It is given that the roots of this equation are real and equal, hence D should be equal...
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Find the condition that one root of the equation ax^2+bx+c=0 is greater than the other by h.

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We have to find the condition for which roots of ax^2 + bx + c = 0 have a difference of h. We know that Difference of roots = √(b²-4ac) / ...
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If alpha and beta are the roots of equation x^2 = x + 1, then find the value of alpha^2/beta - beta^2/alpha.

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We are given the equation x^2 = x + 1 => x^2 - x - 1 = 0 As it is given that the roots of this equation are α, β, we can, by the use o...

If a and b are the root of 10x^2 - 13x +3 =0 find a+b (2) ab (3) a^2+b^2 (4)a^3+b^3 (5) a-b

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a and b are the roots of 10x^2 - 13x + 3 = 0. By using the sum and product of roots formulae, we'll get a + b = -(-13)/10 = 13/10 ab...

If α, β are the roots of 3x^2 +5x-1=0, Construct equations whose root are (i) 5α, 5β (ii) α^2, β^2 (iii) 1/α, 1/β (iv) α+1/β, β+1/α

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It's given that α, β are the roots of equation 3x^2 + 5x - 1 = 0. By applying the sum and product of roots formulae, we'll get α ...
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Two students are solving a quadratic equation of form x^2 + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and -9. Find the correct roots of the equation.

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We are told that the equation is of the form x^2 + px + q = 0. The first guy, who has got the value of p wrong, solves the equation an...

If a^2 + b^2 + c^2 = 2a - 2b - 2, Find the value of 3a - 2b + c.

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We are given that  a^2 + b^2 + c^2 = 2a - 2b - 2 => a^2 + b^2 + c^2 - 2a + 2b + 2 = 0 => a^2 - 2a +1 + b^2 + 2b + 1 + c^2  = 0 =...
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