Question

p(x)=3x²-1,if x=1\√3,2\√3
value bata do please​

Answer 1

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

• p(x) = 3x² - 1 _________(1)

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

• Value of p(x) , when x = 1/√2 & 2/√3

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

First keep , x = 1/√2, in equ(1)

➡ p(1/√2) = 3 × (1/√2)² - 1

➡ p(1/√2) = 3 × 1/2 - 1

➡ p(1/√2) = 3/2 - 1

➡ p(1/√2) = (3-2)/2

➡ p(1/√2) = 1/2

Again, keep x = 2/√3 in equ(1)

➡p(2/√3) = 3 × (2/√3)² - 1

➡p(2/√3) = 3 × 4/3 - 1

➡p(2/√3) = 4 - 1

➡p(2/√3) = 3

$\Large{\underline{\underline{\mathfrak{\red{\bf{Hence}}}}}}$

• Value of p(x) when , x = 1/√2 be 1/2
• Value of p(x) when , x = 2/√3 be = 3

_______________

Answer 2

As we know that x=1/√3,so by the factor theorem,1/√3 is a factor of p(x) if p(1/√3)=0.now,p(1/√3)=3×(1/√3)wholesquare-1.

So,p(x)=1-1. Thus,p(x)=0. Hence,1/√3 is a factor of p(x).