.3 Find the discriminant of the equation 3x2
-2x + ଵ
ଷ
= 0
Answers
Answer:
Answer:
Given:
p(x) = 3x² -5x-2
and zeros 2 and -1/3
To prove : they are the zeros
we know that ,if 'a' is a zero of polynomial p(x) then p(a)=0.Thus, we have to substitute the given numbers in place of x
first ,take x= 2
p(x) = 3x²-5x-2
⇒ p(2) = 3(2²)-5*2-2
= 3*4-10-2
= 12-12
= 0
Hence, 2 is a root (zero) of the given polynomial.
second case , take x = -1/3
p(x)=3x²-5x-2
\begin{gathered}p(\dfrac{-1}{3}) = 3*(\dfrac{-1}{3})^2 -5*\dfrac{-1}{3}-2\\= 3*\dfrac{1}{9} +\dfrac{5}{3}-2\\\\=\dfrac{1}{3}+\dfrac{5-6}{3} [taking\:L.C.M]\\\\\implies \dfrac{1+5-6}{3}=\dfrac{6-6}{3}=\dfrac{0}{3}=0\end{gathered}
p(
3
−1
)=3∗(
3
−1
)
2
−5∗
3
−1
−2
=3∗
9
1
+
3
5
−2
=
3
1
+
3
5−6
[takingL.C.M]
⟹
3
1+5−6
=
3
6−6
=
3
0
=0
Hence, -1/3 is another zero of the polynomial