If `ax^(2)+bx+c=0`, `a ne 0`, `a`, `b`, `c in R` has distinct real roots in `(1,2)`, then `a` and `5a+2b+c` have

Question

If `ax^(2)+bx+c=0`, `a ne 0`, `a`, `b`, `c in R` has distinct real roots in `(1,2)`, then `a` and `5a+2b+c` have

If `ax^(2)+bx+c=0`, `a ne 0`, `a`, `b`, `c in R` has distinct real roots in `(1,2)`, then `a` and `5a+2b+c` have
A. same sign
B. opposite sign
C. not determined
D. none of these

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

If the equation `2x^2+k x y+2y^2=0` represents a pair of real and distinct lines, then find the values of `kdot`

2 Answers 4 Views

Let `l_(1) and l_(2)` be the two skew lines. If P, Q are two distinct points on `l_(1)` and R, S are two distinct points on `l_(2)`, then prove that P

2 Answers 6 Views

if a,b, c, d and p are distinct real number such that `(a^(2) + b^(2) + c^(2))p^(2) - 2p (ab + bc + cd) + (b^(2) + c^(2) + d^(2)) lt 0` then a, b, c,

2 Answers 4 Views

If `x_(1)` and `x_(2)` are the real and distinct roots of `ax^(2)+bx+c=0` then prove that `lim_(xtox1) (1+sin(ax^(2)+bx+c))^((1)/(x-x_(1)))=e^(a(x_(1)

2 Answers 7 Views

Find the values of `a` for which eht equation `||x-2|+a|=4` can have four distinct real solutions.

2 Answers 5 Views

For `a`, `b`,`c` non-zero, real distinct, the equation, `(a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0` has non-zero real roots. One of these roots is als

2 Answers 4 Views

The equation `x^(2)+bx+c=0` has distinct roots. If `2` is subtracted from each root the result are the reciprocal of the original roots, then `b^(2)+c

2 Answers 7 Views

If `ax^2+bx+c=0 and cx^2 + bx+a=0(a,b,c in R)` have a common non-real roots, then which of the following is not true ?

2 Answers 4 Views

If the elements of a matrix `A` are real positive and distinct such that `det(A+A^(T))^(T)=0` then

2 Answers 4 Views

Find the sum of the value (s) of a so that the equation (`x^(2) + 2ax + 2a + 3`) (`x^(2) + 2ax + 4a +5 `) = 0 has only 3 real distinct roots.

2 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
`(a)` Let `x_(1)` and `x_(2)` be two roots of `ax^(2)+bx+c=0`
`1 lt x_(1) lt 2` and `1 lt x_(2) lt 2`
Now, `a(5a+2b+c)=a^(2)(5+2(b)/(a)+(c )/(a))`
`=a^(2)(5+2(-1)(x_(1)+x_(2))+x_(1)x_(2))`
`=a^(2){(x_(1)-2)(x_(2)-2)+1} gt 0`
Hence, `a` and `5a+2b+c` are of same sign.

4 views Answered 2023-02-05 15:29