Question

The values of t for which the quadratic equation $x^2$ + tx + 4 has both roots that are greater than 1, are

• A. t (-5, 4)
• B. t [-5, 4)
• C. t [-5, -4]
• D. t (-5, 4]

Answer 1

The correct option is D

t (-5, 4]

For the equation f(x) = $x^2$ + tx + 4 to have both roots greater than 1

(i) f(1) > 0 [As a > 0]

(ii) D ≥ 0

(iii) 1 < $\frac{\alpha +\beta }{2}$

(i) f(1) > 0 ⇒ 1 + t + 4 > 0 ⇒ t > - 5 ---------- (1)

(ii) D ≥ 0 $\Rightarrow$ $t^2$ - 16 ≥ 0 $\Rightarrow$ t ≤ -4 (or) t ≥ 4 ----------- (2)

(iii) $\frac{-t}{2}$ > 1

t < -2 ----------- (3)

Intersection of (1), (2) & (3) gives t $\in$ (-5, 4)