Question

Determine the nature of the roots of the following quadratic equation from their discriminant: x2 - 2x + 9/4 =0.​

Answer 1

SOLUTION

$\implies \: {x}^{2} - 2x + \frac{9}{4} = 0$

$\implies \: \dfrac{4 {x}^{2} - 8x + 9}{4} = 0$

$\implies \: 4 {x}^{2} - 8x + 9 = 0$

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

$\implies \: d = ( - 8) {}^{2} - 4(4)(9)$

$\implies \: d \: = 64 - 144.$

$\implies \: d \: = - 80$

$\implies \: d \: < 0 \\ \implies roots \: are \: imaginary$

Answer 2

Step-by-step explanation:

$\: \: \sf \rightarrow \: {x}^{2} - 2x + \frac{9}{4} = 0$

Now, take the LCM of the number 4 and 1.

$\: \: \sf \rightarrow \: \frac{4 {x}^{2} - 8x + 9 }{4} = 0$

Now, cross multiplying the number 4.

$\: \: \sf \rightarrow \: 4 {x}^{2} - 8x + 9 = 0 \times4 \\ \\ \: \sf \rightarrow \: 4 {x}^{2} - 8x + 9 = 0$

As we know by quadratic equation here is three terms and we have to find fourth term so now put the terms on their places and let's find fourth term.

$\: \: \sf \: d = {b}^{2} - 4ac \\ \\ \: \sf \: d = {( - 8)}^{2} - 4 \times 4 \times 9 \\ \\ \: \sf \: d = 64 - 144 \\ \\ \: \sf \: d = - 80$

Now, we found the last term so from the last term we know that

$\: \: \sf \implies \: d < 0 = 0 \: is \: greater \: than \: d.$

And Nature of the roots is imaginary and we can imagine it.