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sorry i could answer but right now i am not free
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Q 11
True, it is Rational
Q 12
We have
g(x) = a(x2 + 1) − x(a2 + 1)=
ax2 − a2x − x + a
=ax2 − (a2+1)x + a
Now, zeroes of g(x) are given by solving the equation,
g(x) = 0⇒ax2 − a2x − x + a = 0
⇒ax(x − a) − 1(x − a) = 0
⇒(ax − 1)(x − a) = 0
⇒ax − 1 = 0 or x − a = 0
⇒x = 1a or x = a
Sum of zeroes= 1/a + a = 1+a^2/a = −coefficient x/coefficient of x^2
Product of zeroes = 1/a×q= 1 = coefficient term/coefficient of x^2
Q13
False
Q14
True, 0.115
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