`a gt b gt0"and"2x^2-a x-b^2=0"t h e n"` (A) both roots lie between `-a/2` and a (B) both roots are positive (C) both roots are negative (D) both roots are imaginary

For what values of m the equation (1+m)x^(2)-2(1+3m)x+(1+8m)=0 has (m in R) (i) both roots are imaginary? (ii) both roots are equal? (iii) both roots are real and distinct? (iv) both roots are positive? (v) both roots are negative? (vi) roots are opposite in sign? (vii)roots are equal in magnitude but opposite in sign? (viii) atleast one root is positive? (ix) atleast one root is negative? (x) roots are in the ratio 2:3 ?

For what values of m the equation (1+m)x^(2)-2(1+3m)x+(1+8m)=0 has (m in R) (i) both roots are imaginary? (ii) both roots are equal? (iii) both roots are real and distinct? (iv) both roots are positive? (v) both roots are negative? (vi) roots are opposite in sign? (vii)roots are equal in magnitude but opposite in sign? (viii) atleast one root is positive? (iv) atleast one root is negative? (x) roots are in the ratio 2:3 ?

If a,b,c epsilon R and abgt0, a+2b+4c=0 then equation ax^2+bx+c=0 has (A) both roots positive (B) both roots negative (C) one positive and one negative root (D) both roots imginary

Let x^2-2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then find the value of 'a' for which (a) Both the roots are positive (b)Both the roots are negative (c) Both the roots are opposite in sign. (d) Both the roots are greater than 1. (e)Both the roots are smaller than 1. (f) One root is small than 1 and the other root is greater than 1.

If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary