Equations Reducible to Quadratic

JEE Main Mathematics · Quadratic Equations · 11 questions, latest first

• The smallest positive integral value of a, for which all the roots of x^4-a x^2+9=0 are real and distinct, is equal to202624 January, Shift 2 · Q3
• If α and β(α<β) are the roots of the equation (-2+√3)(|√x-3|)+(x-6 √x)+(9-2 √3)=0, x ≥ 0, then √((β)/(α))+√(α β) is equal to:202623 January, Shift 1 · Q2
• The number of solutions of the equation (9/x-9/(√x)+2)(2/x-7/(√x)+3)=0 is:202529 January, Shift 1 · Q3
• The product of all the rational roots of the equation (x^2-9 x+11)^2-(x-4)(x-5)=3, is equal to202524 January, Shift 1 · Q2
• The sum of all the solutions of the equation (8)^2 x-16 ·(8)^x+48=0 is:20248 April, Shift 1 · Q3
• Let S={x ∈ R:(√3+√2)^x+(√3-√2)^x=10}. Then the number of elements in S is:20241 February, Shift 1 · Q2
• The number of points, where the curve f(x)=e^8 x-e^6 x-3 e^4 x-e^2 x+1, x ∈ R cuts x -axis, is equal to ____202311 April, Shift 2 · Q24
• Let S={x: x ∈ R. and.(√3+√2)^x^2-4+(√3-√2)^x^2-4=10}. Then n(S) is equal to20231 February, Shift 1 · Q63
• The equation e^4 x+8 e^3 x+13 e^2 x-8 e^x+1=0, x ∈ R has:202331 January, Shift 2 · Q63
• The number of real roots of the equation √(x^2-4 x+3)+√(x^2-9)=√(4 x^2-14 x+6), is:202331 January, Shift 1 · Q62
• The number of real solutions of the equation 3(x^2+1/x^2)-2(x+1/x)+5=0, is202324 January, Shift 2 · Q62