Solve Q21 & 22 showing clearly all steps 21Find the value(s) of the constant k, for which the roots of the equationx -2(1 + 3k) x + 7(2k + 3)=0 are equal42. Find the range of values of the constant k for which the quadratic equation:x + x + k –- 12 = 0,has real and distinct roots.23. The roots of the quadratic equation x² – x + 2 = 0 are aand B. Prove that-111(a)1+ a?1+ B211(b)1+ a?1+ B221and1+ B21Hence form a quadratic equation whose roots are1+ a223.Find the value of the constant k for which the equationx² + (k + 1)x + k = 0 has one root double the other,||

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21 Find the value(s) of the constant k, for which the roots of the equation x -2(1+ 3k) x + 7(2k + 3) =0 are equal 22. Find the range of values of the constant k for which the quadratic equation: x + x + k2 - 12 = 0,has real and distinct roots. %3D 23. The roots of the quadratic equation x2 - x + 2 = 0 are aand B. Prove that 1 1 (a) 1+ a? 1+ B2