Question

9.Find the zeroes of P(x) = 4x2 – 12x – 7. And also verify the relationship of zeroes and
its coefficient.​

Answer 1

Answer:

zeroes are 7/2 and -1/2

Step-by-step explanation:

$4x^2-12x-7\\4x^2-14x+2x-7\\2x(2x-7)+1(2x-7)\\(2x-7)(2x+1)\\2x-7=0\ and\ 2x+1=0\\x=\frac{7}{2}\ and\ x=\frac{-1}{2}$

Now, we know that

$Sum\ of\ zeroes=\ \frac{-coefficient\ of\ x}{coefficient\ of\ x^2}\ \ also\ \ Product\ of\ zeroes=\ \frac{constant\ term}{coefficient\ of\ x^2}$

$\therefor\ \frac{7}{2}+\frac{-1}{2}=\frac{-(-12)}{4}\ \ and\ \ \frac{7}{2}\times\frac{-1}{2}=\frac{-7}{4}$

$\frac{6}{2}=\frac{12}{4}\ \ and\ \ \frac{-7}{4}=\frac{-7}{4}$

$3=3\ \ and\ \ \frac{-7}{4}=\frac{-7}{4}$

LHS=RHS   and LHS = RHS

So, relationship of zeroes with the coefficients is verified.