x²+4√3x-63=0 solve by factorisation method
Answers
Step-by-step explanation:
x²+4√3x - 63 =0
=. By splitting the middle term
Solve by factorization:
x^{2} + 4\sqrt{3} - 63x
2
+4
3
−63
Solution:
p(x) = x^{2} + 4\sqrt{3}x - 63p(x)=x
2
+4
3
x−63
To factorize p(x)
\begin{gathered}p(x) = x^{2} + 4\sqrt{3} - 63 = 0 \\ \implies x^{2} - 3\sqrt{3}x + 7\sqrt{3}x - 63 = 0 \\ \implies x(x - 3\sqrt{3}) + 7\sqrt{3}(x - 3\sqrt{3}) = 0 \\ \implies (x+7\sqrt{3})(x-3\sqrt{3}) = 0\end{gathered}
p(x)=x
2
+4
3
−63=0
⟹x
2
−3
3
x+7
3
x−63=0
⟹x(x−3
3
)+7
3
(x−3
3
)=0
⟹(x+7
3
)(x−3
3
)=0
\begin{gathered}x + 7\sqrt{3} = 0 \\ x = -7\sqrt{3}\end{gathered}
x+7
3
=0
x=−7
3
\begin{gathered}x-3\sqrt{3} = 0 \\ x = 3\sqrt{3}\end{gathered}
x−3
3
=0
x=3
3
Therefore, zeroes of p(x) = x^{2} + 4\sqrt{3}x - 63p(x)=x
2
+4
3
x−63 are -7\sqrt{3}−7
3
and 3\sqrt{3}3
3
.