wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If f(x),g(x) and h(x) are three polynomial of degree 2 and Δ(x)=∣ ∣ ∣f(x)g(x)h(x)f(x)g(x)h(x)f′′(x)g′′(x)h′′(x)∣ ∣ ∣, then Δ(x) is a polynomial of degree 2, if true enter 1 else 0.

Open in App
Solution

Let f(x)=a0x2+a1x+a2g(x)=b0x2+b1x+b2h(x)=c0x2+c1x+c2
Then, Δ(x)=∣ ∣f(x)g(x)h(x)2a0x+a12b0x+b12c0x+c12a02b02c0∣ ∣
=x∣ ∣f(x)g(x)h(x)2a02b02c02a02b02c0∣ ∣+∣ ∣f(x)g(x)h(x)a1b1c12a02b02c0∣ ∣
=0+2∣ ∣f(x)g(x)h(x)a1b1c1a0b0c0∣ ∣
=2[(b1c0b0c1)f(x)(a1c0a0c1)g(x)+h(x)(a1b0a0b1)]
Hence degree of Δ(x)2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon