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Let ? and ? be the roots of the equation x2 - ax - bx + ab - c = 0. What is the quadratic equation whose roots are a and b?
Formula used:If ? and ? are the roots of quadratic equation ax2 + bx + c = 0Sum of root ? + ? = -b/aProduct of root ?? = c/aEquations with root ? and ? can be written asx2 - (? + ?)x + ?? = 0Calculation: Given that, ? and ? be the roots of the equation x2 - ax - bx + ab - c = 0 ? x2 - (a + b)x + (ab - c) = 0 Hence, sum of root ? + ? = a + b -----(1)Product of root?? = ab - c? ab = ?? + c -----(2)Hence, quadretic equation with root a & b is x2 - (a + b)x + ab = 0 Put the value from the equation (1) & (2).? x2 - (? + ?)x + ?? + c = 0? x2 - ?x - ?x + ? ? + c = 0
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