Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202319 May 2023Morning ShiftMathematicsQuadratic EquationActual

If k kx +3 + 3 3 x - k = 12 x +5 ( kx +3)(3 x - k ) x R - 3 k , k 3 , then both the roots of the equation kx ^2-7 x +3=0 are

Options

  1. ARational numbers
  2. BIrrational numbers
  3. CComplex numbers
  4. DIntegers

Correct answer

A. Rational numbers

Step-by-step solution

Given, aligned & k (k x+3) + 3 (3 x-k) = 12 x+5 (k x+3)(3 x-k) & k(3 x-k)+3(k x+3)=12 x+5 & 6 x k-k^2+9=12 x+5 aligned Comparing both side, we get 6 k=12 k=2 Hence, k x^2-7 x+3=0 aligned & 2 x^2-7 x+3=0 & 2 x^2-6 x-x+3=0 & 2 x(x-3)-1(x-3)=0 & (2 x-1)(x-3)=0 & x= 1 2 , 3 aligned Hence roots are rational numbers.

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

If is the common root of the quadratic equations x^2-5 x+4 a=0 , x^2-2 a x-8=0 , where a R , then the value of ^4- ^3+68 is 2025If , are the roots of x^2-5 x-6 =0 and , are the roots of x^2-5 x-6 =0 , then + + + = 2025If , , are the roots of the equation x ^3+ px ^2+ qx + r =0 , then ( + )( + )( + )= 2025Let f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2, x R . If b and c are nonzero real numbers such that f(x)> g(x) , then | c b | lies in the interval 2025If x ^2-4 ax +5+ a >0 for all x R whenever a ( , ) , then 4 + = 2025If , , are the roots of the equation x^3-12 x^2+k x-18=0 and one of them is thrice the sum of the other two roots, then ^2+ ^2+ ^2-k= 2025The polynomial equation of degree 5 whose roots are the roots of the equation x^5-3 x^4-x^3+11 x^2-12 x+4=0 each increased by 2, is 2025If the difference of the roots of the equation x^2-7 x+10=0 is same as the difference of the roots of the equation x ^2-17 x + k =0 , then a divisor of k is 2025 Full Quadratic Equation list All AP EAMCET PYQs