Question

2.
If one root of the equation 2x2 – 3x + c = 0 is 1, then other root is
(a) -1, (b) 2, c) { (d) none of these.​

Answer 1

Answer :

1/2

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; ax² + bx + c = 0

★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

Solution :

Here ,

The given quadratic equation is ;

2x² - 3x + c = 0

Now ,

Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 , we get ;

a = 2

b = -3

c = c

Also ,

It is given that one of the root of the given quadratic equation is 1 .

Thus ,

Let α = 1 and ß be the roots of the given quadratic equation .

Also ,

We know that , sum of the roots of the given quadratic equation will be given as ;

=> α + ß = -b/a

=> 1 + ß = -(-3)/2

=> 1 + ß = 3/2

=> ß = 3/2 - 1

=> ß = (3-2)/2

=> ß = 1/2

Hence ,

The other root of the given quadratic equation is ½ .

Answer 2

Required answer -

Question -

★ If one root of the equation 2x² – 3x + c = 0 is 1, then other root is (Options are given below) –

• a) -1

• b) 2

• c) ½

• d) None of these

Given that -

★ One root of the quadratic equation 2x² - 3x + c = 0

To find -

★ Other root (atq)

Solution -

★ Other root is ½

Using concept -

★ How the sum of roots of quadratic equation is given.

Using dimension -

★ α + ß = -b/a

Full solution -

~ As it's given that one root of the quadratic equation 2x² - 3x + c = 0. So now there is a need to compare them like the following,

ax² + bx + c = 0

(We use this equation here because it is the general form of quadratic equation).

Here,

• a = 2

• b = -3

• c = c

~ In this question it is also given that the root of a quadratic equation is 1 and we have to find the other root. Henceforth,

~ Let α and ß as the roots of the given equation.

Here,

☑️ α is 1

☑️ ß is ? [to find]

Henceforth,

➝ α + ß = -b/a

➝ 1 + ß = -(-3)/2

• - cancel -

➝ 1 + ß = 3/2

• (+ = -) ; (- = +)

➝ ß = 3/2 - 1

• LCM

➝ ß = (3-2) / 2

➝ ß = ½

Henceforth, ½ is the other root of the given quadratic equation..!