AP EAMCET202318 May 2023Evening ShiftMathematicsQuadratic EquationActual

If cosec , and are the roots of cx ^2+ bx + a =0(b c 0) , then b^2 (b^2-4 a c )=

Options

A-2 c^4
B2 c^4
C-c^4
Dc ^4

Correct answer

D. c ^4

Step-by-step solution

cx ^2+ bx + a =0 Let = cosec & = + =- b c & = a c aligned & Now, ^2- ^2=( + )( - ) & cosec ^2 - ^2 =- b c ( + )^2-4 & 1=- b c b^2 c^2 - 4 a c & 1=- b c b^2-4 a c c^2 b^2-4 a c c^2 =- c b & b^2-4 a c c^2 = c^2 b^2 b^2 (b^2-4 a c )=c^4 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 2025 If , are the roots of x^2-5 x-6 =0 and , are the roots of x^2-5 x-6 =0 , then + + + = 2025 If , , are the roots of the equation x ^3+ px ^2+ qx + r =0 , then ( + )( + )( + )= 2025 Let 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 2025 If x ^2-4 ax +5+ a >0 for all x R whenever a ( , ) , then 4 + = 2025 If , , 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= 2025 The 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 2025 If 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