Fill in the Blanks

Mathematics

Chapter 4: Quadratic Equations

Class 10

Fill in the blanks Mathematics Chapter 4: Quadratic Equations for Class 10th is very important as these type of questions help in scoring good marks. Fill in the blanks type questions are to be answered to the point and hence very helpful in overall scoring. Fill  in the blanks Type of questions helps students to think Critically on every aspects of life.

Here is a collection of few questions for CBSE Class 10th Term 2 Exams. These Fill in the blanks are fully solved. 

Fill in the Blanks with suitable words or expressions.

Question.1.
If a, b are the roots of `x^{2}+x+1=0`, then `a^{2}+b^{2}`= _________

Question.2.
If a, b are the roots of `x^{2}+bx+c=0` and `\alpha +h, \beta +h` are the roots of `x^{2}+qx+r=0`, then h = ______

`\frac{1}{2}(b-q)`

Question.3.
If the discriminant of a quadratic equation is zero, then its roots are _________ and _________.

real, equal

Question.4.
A polynomial of degree 2 is called the __________ polynomial.

quadratic

Question.5.
Let `ax^{2}+bx+c=0`, where a, b, c are real numbers, `a\neq 0`, be a quadratic equation, then this equation has no real roots if and only if ___________

`b^{2}<4ac`

Question.6.
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides are _______

5 cm, 12 cm

Question.7.
A quadratic equation cannot have more than ___________ roots.

Question.8.
The equation `ax^{2}+bx+c=0`, `a ≠ 0` has no real roots, if ____________

`b^{2}<4ac`

Question.9.
If the product ac in the quadratic equation `ax^{2}+bx+c=0` is negative, then the equation cannot have ________ roots.

Non-real

Question.10.
A real number `\alpha` is said to be __________ of the quadratic equation `ax^{2}+bx+c=0`, if `a(\alpha)^{2}+b(\alpha)+c=0`.

Question.11.
A quadratic equation does not have any real roots if the value of its discriminant is _________ zero.

less than

Question.12.
The values of `k` for which the equation `2x^{2}+kx+x+8=0` will have real and equal roots are ________

7 and -9

Question.13.
For any quadratic equation `ax^{2}+bx+c=0`, `b^{2}-4ac`, is called the __________ of the equation.

discriminant

Question.14.
A quadratic equation `ax^{2}+bx+c=0` has two distinct real roots, if `b^{2}-4ac` __________

Question.15.
The roots of a quadratic equation is same as the _________ of the corresponding quadratic polynomial.

Question.16.
A quadratic equation in the variable `x` is of the form `ax^{2}+bx+c=0`, where a, b, c are real numbers and a _______ 

`≠ 0`

Question.17.
If the discriminant of a quadratic equation is greater than zero, then its roots are _______ and ______.

real, distinct

Question.18.
The equation of the form `ax^{2}+bx=0` will always have __________ roots.

Question.19.
The equation `x^{2}+x-5=0` then, product of its two roots is __________

Question.20.
The quadratic equation whose roots are the sum and difference of the squares of roots of the equation `x^{2}-3x+2=0` is ___________

`x^{2}-8x+15=0`

Question.21.
If r, s are roots of `ax^{2}+bx+c=0`, then `\frac{1}{r^{2}}+\frac{1}{s^{2}}` is __________.

`\frac{b^{2}-2ac}{c^{2}}`

Question.22.
If `\alpha, \beta` are roots of the equation `ax^{2}+bx+c=0`, then the quadratic equation whose roots are `a\alpha + b` and `a\beta + b` is __________

`x^{2}-bx+ca=0`

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