JEE Advanced Mathematics: Quadratic Equations Practice Questions

14 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$I f o n er oo t o f t h ee q u a t i o n x^{2} - 5 x + k = 0 i s 2, f in d t h e v a l u eo f k .$
Easy
Q2.
$F in d t h es u m o f t h er oo t so f t h e q u a d r a t i ce q u a t i o n x^{2} - 7 x + 12 = 0.$
Easy
Q3.
$W ha t i s t h e d i scr iminan t o f t h e q u a d r a t i ce q u a t i o n 2 x^{2} - 4 x + 1 = 0 ?$
Easy
Q4.
$W hi c h o f t h e f o l l o w in g i s a r oo t o f t h ee q u a t i o n x^{2} - 9 = 0 ?$
Easy
Q5.
$F in d t h e p r o d u c t o f t h er oo t so f t h ee q u a t i o n 3 x^{2} + 2 x - 5 = 0.$
Easy
Q6.
$T h ese t o f a l l v a l u eso f k f or w hi c h t h e q u a d r a t i ce q u a t i o nk x^{2} + 2 x + 1 = 0 ha sr e a l an dd i s t in c t r oo t s i s$
Medium
Q7.
$I f t h er oo t so f t h ee q u a t i o n x^{2} - b x + c = 0 a r e tw oco n sec u t i v e in t e g er s, t h e n b^{2} - 4 c i se q u a l t o$
Medium
Q8.
$I f a l p haan d b e t aa r e t h er oo t so f x^{2} - p (x + 1) - c = 0, t h e n t h e v a l u eo f (a l p h a^{2} + 2 a l p ha + 1) / (a l p h a^{2} + 2 a l p ha + c) + (b e t a^{2} + 2 b e t a + 1) / (b e t a^{2} + 2 b$
Medium
Q9.
$L e t a l p haan d b e t ab e t h er oo t so f t h ee q u a t i o n x^{2} - 6 x + 2 = 0. I f a_{n} = a l p h a^{n} - b e t a^{n} f or n >= 1, t h e n t h e v a l u eo f (a_{1} 0 - 2 a_{8}) / (2 a_{9}) i se q u a l t o$
Medium
Q10.
$T h e n u mb er o f r e a l so l u t i o n so f t h ee q u a t i o n x^{2} - 2∣ x ∣ - 3 = 0 i s$
Medium
Q11.
$I f t h ee q u a t i o n x^{2} + a x + b = 0 ha sr e a l r oo t s a l p haan d b e t a, an d t h ee q u a t i o n x^{2} + c x + d = 0 ha sr e a l r oo t s a l p ha + 1 an d b e t a + 1, t h e n t h e v a l u eo f (a - c)$
Hard
Q12.
$I f a l p haan d b e t aa r e t h er oo t so f x^{2} - p x + q = 0 an d a l p h a^{4}, b e t a^{4} a r e t h er oo t so f x^{2} - r x + s = 0, t h e n t h e v a l u eo f r in t er m so f p an d q i s :$
Hard
Q13.
$L e t a l p haan d b e t ab e t h er oo t so f t h ee q u a t i o n x^{2} - 6 x + 1 = 0. I f a_{n} = a l p h a^{n} - b e t a^{n} f or n >= 1, t h e n t h e v a l u eo f (a_{1} 0 - 2 a_{8}) / (2 a_{9}) i se q u a l t o :$
Hard
Q14.
$L e t f (x) = x^{2} + a x + b . I f t h er oo t so f f (x) = 0 a r er e a l an dd i f f er b y a t m os t 1, t h e n t h e minim u m v a l u eo f a^{2} - 4 bi s :$
Hard

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