Question

Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial x²-x-6​

Answer 1

Zeros of this function

• x²-x-6=0
• x²-3x+2x-6=0
• x(x-3)+2(x-3)=0
• (x+2)(x-3)=0
• x={-2,3}

ZEros of reciprocal function

• x={-1/2,1/3}

The equation

• x²-(-1/2+1/3)x-(1/2)(1/3)=0
• x²-1/6x-1/6=0