Q 41 a b 0 and 2x2-ax-b2=0 then (A) both roots lie between -a2 and - Maths - Complex Numbers and Quadratic Equations

Question

Q 41 a > b > 0 and 2 x 2 - a x - b 2 = 0 then
(A) both roots lie between - a 2 and a
(B) both roots are positive
(C) both roots are negative
(D) both roots are imaginary

Aarushi Mishra · Accepted Answer

Let fx=2x2-ax-b2=0Since coefficent of x>0, therefore, it is an upward parabola
Vertex of parabola a'x2+b'x+c' i given by x=-b'2a'Discriminant D=b'2-4a'c'=a2+8b2>0It has real and distinct rootsHereVertex=--a4=a4f-a2=2-a22+a22-b2=2a24+a22-b2=a22+a22-b2=a2-b2Since a>b>0a2>b2a2-b2>0f-a2>0fa=2a2-a2-b2=a2-b2fa>0Hence this means that the roots lie between -a2, and a
 
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Q.41. a > b > 0 and 2 x 2 - a x - b 2 = 0 then (A) both roots lie between - a 2 and a (B) both roots are positive (C) both roots are negative (D) both roots are imaginary

Q.41. a > b > 0 and $2 x^{2} - a x - b^{2} = 0$ then
(A) both roots lie between $- \frac{a}{2}$ and a
(B) both roots are positive
(C) both roots are negative
(D) both roots are imaginary