Question

The zeroes of the quadratic polynomial x²-5x+6 are *
Both equal
One positive and one negative
Both positive
Both nega​

Answer 1

Answer:

both negative is the answer

Answer 2

Step-by-step explanation:

Using factorisation method,

$x²-5x+6$

$x²-3x - 2x+6$

$x(x - 3) \: - 2(x - 3)$

$(x - 3)(x - 2) = 0$

$x - 3 = 0 \\ x = 3$

$x - 2 = 0 \\ x = 2$

Hence the roots are 3 and 2

Alternate method, using Sridharacharya formula,

$D = {b}^{2} - 4 \: ac$

${ - 5}^{2} - 4 \times 1 \times 6$

$25 - 25 = 1$

$\frac{- b \frac{ + }{ - } \sqrt{D}}{2a}$

$\frac{ - ( - 5) \frac{ + }{ - } \sqrt{1} }{2 \times 1}$

$\frac{5 + 1}{2} \: \: \: \: \: \: or \: \: \: \: \: \: \: \frac{5 - 1}{2}$

$\frac{6}{2} \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \frac{4}{2}$

$3 \: \: \: \: \: \: or \: \: \: \: \: \: \: \: 2$

Hence the roots are 3 and 2