NCERT Class 10 Math Quadratic Equation Exercise 4.3

Hi Friends and Champs!

Before We start next exercise, need to give some attention on below considerations:

As you know the general equation of a quadratic equation is:

ax² + bx + c = 0 , a ≠ 0

solve this equation to find the roots or Zeroes for "x" .

In above result roots or ZEROES of the general equation ax² + bx + c = 0 , a ≠ 0 depend on the value of (b²- 4ac) called Discriminant .

Now we have 3 cases in this scenario.

Ist Case : When discriminant ( b²- 4ac ) > 0 , Roots will be real and distinct.

2nd Case : When discriminant ( b²- 4ac ) = 0, Roots will be identical and real.

3rd Case : When discriminant ( b²- 4ac ) < 0 , Roots will be imaginary and distinct.

Exercise: 4.3

1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

(i) 2x² – 3x + 5 = 0 (ii) 3x² – 4 3 x + 4 = 0 (iii) 2x² – 6x + 3 = 0

Solution:

(i) 2x² – 3x + 5 = 0

(ii) 3x² – 4 3 x + 4 = 0

(iii) 2x² – 6x + 3 = 0

2. Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(i) 2x² + kx + 3 = 0 (ii) kx (x – 2) + 6 = 0

3. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.

4. Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

5. Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

Pls comment, if you have any doubt in any question or if need a solution for related exercise queries.

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