If the roots of the quadratic equation x2-p x-q-0 are tan 30- and tan 15- respectively- then value of 2-q-p isA- 3B- 0C- 1D- 2

The correct option is A 3x^2 + px + q = 0 Sum of roots = tan 30^∘ + tan 15^∘ = p Product of roots = tan 30^∘. tan 15^∘ = q tan 45^∘ = tan 30^∘ + tan 15^∘/1 t ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Mathematics

Relation between Roots and Coefficients for Quadratic

If the roots ...

Question

If the roots of the quadratic equation $x^{2} + p x + q = 0$ are tan $30^{\circ}$ and tan $15^{\circ}$ , respectively, then value of 2 + q - p is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0.0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 3
$x^{2} + p x + q = 0$
Sum of roots = tan $30^{\circ} + t a n 15^{\circ} = - p$
Product of roots = $t a n 30^{\circ} . t a n 15^{\circ} = q$
$t a n 45^{\circ} = \frac{t a n 30^{\circ} + t a n 15^{\circ}}{1 - t a n 30^{\circ} . t a n 15^{\circ}} = \frac{- p}{1 - q} = 1 \Rightarrow - p = 1 - q \Rightarrow q - p = 1 ∴ 2 + q - p = 3$

Suggest Corrections

Similar questions

Q. If the roots of the quadratic equation

x^{2} + p x + q = 0

are

t a n 30^{\circ}

and

t a n 15^{\circ}

, respectively, then the value of

2 + q - p

is :

Q. If the roots of the quadratic equation

x^{2} + p x + q = 0

are tan

30^{\circ}

and tan

15^{\circ}

, respectively, then value of 2 + q - p is

Q. If the roots of the quadratic equation

x^{2} + p x + q = 0

are

tan 30^{\circ}

and

tan 15^{\circ}

, respectively then the value of

2 + q - p

Q. If the roots of quadratic equation

x^{2} + p x + q = 0

are

t a n 30^{\circ}

and

t a n 15^{\circ}

, respectively then the value of

2 + q - p

is -

Q. lf the roots of quadratic equation

x^{2} + p x + q = 0

are

tan 30^{0}

and

tan 15^{0}

respectively, then the value of

2 + q - p

is:

Join BYJU'S Learning Program

If the roots of the quadratic equation x2+px+q=0 are tan 30∘ and tan 15∘, respectively, then value of 2 + q - p is

The correct option is B 3x2+px+q=0 Sum of roots = tan 30∘+tan 15∘=−p Product of roots = tan 30∘.tan 15∘=q tan 45∘=tan 30∘+tan 15∘1−tan 30∘.tan 15∘=−p1−q=1⇒−p=1−q⇒q−p=1∴2+q−p=3

If the roots of the quadratic equation $x^{2} + p x + q = 0$ are tan $30^{\circ}$ and tan $15^{\circ}$ , respectively, then value of 2 + q - p is