Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202018 Sep 2020Evening ShiftMathematicsQuadratic EquationActual

For how many values (a C ), the equations (x^2-8 x+7=0 ) and (x^2-2 a x+49=0 ) have a common root?

Options

  1. A1
  2. B3
  3. C2
  4. D0

Correct answer

C. 2

Step-by-step solution

Let ( ) be the common root of given Equations ( aligned & ^2-8 +7=0 (i) & ^2-2 a +49=0 (ii) aligned ) From Eq (i). - Eq. (ii) ( aligned (-8+2 a) -42 & =0 2(-4+a) & =42 & = 21 a-4 aligned ) On putting value of ( ) in Eq. (i), ( aligned ( 21 a-4 )^2-8 ( 21 a-4 )+7 & =0 441-168(a-4)+7(a-4)^2 & =0 441-168 a+672+7 (a^2+16-8 a ) & =0 7 a^2-224 a+1225 & =0 aligned ) Here, (D > 0 ) ( ) Above quadratic equation have two distinct real roots. ( ) Number of possible value of (a ) are 2. Hence, option (c) is correct.

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