solve plzzzz

Question

6. p, q, r are given real numbers. Consider the polynomials (q-r)(x-q)(x-r) + (r-p)(x-r)(x-p) + +(p-q)(x-p)(x-q) + k for all real k. Then [ ]

A) there exists a k such that the degree of the polynomial is 2

B) there exists a k such that the degree of the polynomial is 1

C) there exists no k such that the degree of the polynomial is 0

D) there exists no k such that the degree of the polynomial is undefined

E) none of these

sir plzzzzzzzz solve .... i will surely approve.....

Pushkar Pandit · Accepted Answer

(q-r)(x-q)(x-r) + (r-p)(x-r)(x-p) + (p-q)(x-p)(x-q) + k

-->first let us solve

(q-r)(x-q)(x-r)

we will get,

qx^2-q^2x-rx^2+rqx-rqx+rq^2+r^2x-r^2q

x^2(q-r)+(r^2-q^2)x+rq(q-r)

Now solve

(r-p)(x-r)(x-p)

Here we can see the similar pattern i.e.Herein place of "q" it is "r" and in place of "r" it is "p".So,we can write

x^2(r-p)+(p^2-r^2)x+rp(r-p)

Similarly,3rd erm also folows similar pattern So

x^2(p-q)+(q^2-p^2)x+qp(p-q)

When we will add all the 3 terms it will sum out to 0and only 'k' is left

As 'k' is a constant so the possible degree of polynomial is 0

It is satisfying only fifth option so answer is none of these

Magical Mathematics[Interesting Approach]> solve plzzzz...

iit jee , 14 Years ago

Pushkar Pandit

LIVE ONLINE CLASSES

Given that (1+5x)⁴ = 1 + Px + Qx² + Rx³ +..... Find the values of P - 2Q + 3R

magical mathematics[interesting approach]

9 men and 15 boys working 10 hours a day can make 12 pillars in 42 days, in how many days will 12 men and 22 boys working 8 hours a day can make pillars 4 times the previous number?

magical mathematics[interesting approach]

In the given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter, find angle PCA + angle BCQ?

magical mathematics[interesting approach]

for any two sets A and B (A-B)U(B-A)U (A intersection B)

magical mathematics[interesting approach]

If someone has got 150 out of 200 marks in term 1 exam and 160 out of 200 marks in term 2 exam then what is the percentage in 30:70

magical mathematics[interesting approach]

Magical Mathematics[Interesting Approach]> solve plzzzz...

iit jee , 14 Years ago

Pushkar Pandit

LIVE ONLINE CLASSES

Other Related Questions on magical mathematics[interesting approach]

Given that (1+5x)⁴ = 1 + Px + Qx² + Rx³ +..... Find the values of P - 2Q + 3R

magical mathematics[interesting approach]

9 men and 15 boys working 10 hours a day can make 12 pillars in 42 days, in how many days will 12 men and 22 boys working 8 hours a day can make pillars 4 times the previous number?

magical mathematics[interesting approach]

In the given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter, find angle PCA + angle BCQ?

magical mathematics[interesting approach]

for any two sets A and B (A-B)U(B-A)U (A intersection B)

magical mathematics[interesting approach]

If someone has got 150 out of 200 marks in term 1 exam and 160 out of 200 marks in term 2 exam then what is the percentage in 30:70

magical mathematics[interesting approach]