1.

Find the zeros of x2-4x+4 and compare with coefficient

Answer»

f(x) ={x}^{2} - 4x + 4 \\ to \: find \: zeroes \: we \: put \: f(x) = 0 \\ {x}^{2} - 4x + 4 = 0 \\ {x }^{2} - 2x - 2x + 4 = 0 \\ x(x - 2) - 2(x - 2) = 0 \\ (x - 2)(x - 2) = 0 \\

HENCE the ROOTS are 2,2

Comparison with COEFFICIENTS :-

sum \: of \: roots = \frac{ - (co-efficient \: of \: x )}{co-efficient \: of \: {x}^{2} } \\ 2+2= \frac{ - ( - 4)}{1} \\ 4=4 \\ product \: of \: roots = \: \frac{constant \: term}{co-efficient \: of \: {x}^{2}} \\ 2 \times 2 = \frac{4}{1} \\ 4 = 4

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