Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20228 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

If x^2+p x+1 is a factor of a x^3+b x+c , then

Options

  1. Aa^2+c^2=a b+3
  2. Ba^2-c^2=a b
  3. Ca^2-c^2=-a b
  4. Da^2+c^2=a b

Correct answer

B. a^2-c^2=a b

Step-by-step solution

array r a x-a p x ^ 2 + p x + 1 a x ^ 3 + b x + c ax ^3+ apx ^2+a x - - - - apx ^2+( b - a ) x + c - apx ^2- ap ^2 x - ap + + + ( ba + ap ^2 ) x + ap + c array Since x^2+P x+1 is factor of a x^3+b x+c a p+c=0 p=- c a ...(i) and n-a+a p^2=0 n - a + a c ^2 a ^2 =0 [ from (i) ] aligned & a b-a^2+c^2=0 & a b=a^2-c^2 aligned

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