Question

The quadratic equation 2x²-5x+1=0 has (a) Two distinct real roots (b) No real roots (c) Two equal roots (d) More than two roots​

Answer 1

Answer:

$\begin{aligned} D &=(\sqrt{5})^{2}-4 \cdot 2 \cdot 1 \\ &=5-8 \\ &=-3 \\ D &<0 \end{aligned}</p><p>\begin{array}{l} D=b^{2}-4 a c \\ a=2, b=\sqrt{5}, c=1 \end{array}</p><p>Step 2: Find the value of discriminant from the givenequation</p><p>2 x^{2}-\sqrt{5} x+1=0</p><p>It is given as </p><p>Step 1:Write the given information$

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The quadratic equation 2x² - 5x + 1 = 0 has

(a) Two distinct real roots

(b) No real roots

(c) Two equal roots

(d) More than two roots

EVALUATION

Here the given Quadratic equation is

$\displaystyle \sf{ 2{x}^{2} - 5x + 1 = 0 }$

So the equation has exactly two roots

We find the roots as below

$\displaystyle \sf{ 2{x}^{2} - 5x + 1 = 0 }$

$\displaystyle \sf{ \implies x = \frac{ - ( - 5) \pm \: \sqrt{ {( - 5)}^{2} - 4 \times 2 \times 1 } }{2 \times 2} }$

$\displaystyle \sf{ \implies x = \frac{ 5 \pm \: \sqrt{ 25 - 8 } }{4} }$

$\displaystyle \sf{ \implies x = \frac{ 5 \pm \: \sqrt{ 17 } }{4} }$

Thus the roots are real and distinct

FINAL ANSWER

Hence the correct option is

(a) Two distinct real roots

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ find the equation that formed by increasing each root of 2x²-3x-1=0by 1

https://brainly.in/question/33063519

2. find the equation that formed by squaring each root of the equation x²+3x-2=0

https://brainly.in/question/33064705