If a x 2 + b x + c = 0 is a quadratic equation where a , b , c belongs to the real number a ≠ 0 then check a x 2 - b x + c = 0 is a quadratic equation or not. Give reason

We know that a x 2 + b x + c is a two-degree polynomial in one variable (where a , b , c are real numbers and a ≠ 0 ). It is known as a quadratic polynomial. If we equate this quadratic polynomial equal zero it becomes a quadratic equation. Given equation is a x 2 - b x + c = 0 , where a , - b , c are real number and a ≠ 0 . Therefore, the equation a x 2 - b x + c = 0 is quadratic equations.

If a x 2 + b x + c = 0 is a quadratic equation where a , b , c belongs to the real number a ≠ 0 then check b x + c = 0 is a quadratic equation or not. Give reason

We know that a x 2 + b x + c is a two-degree polynomial in one variable (where a , b , c are real numbers and a ≠ 0 ). It is known as a quadratic polynomial. If we equate this quadratic polynomial equal zero it becomes a quadratic equation. Given equation is b x + c = 0 , where b , c are real number and a = 0 . Therefore, the equation b x + c = 0 is not a quadratic equation.

If a x 2 + b x + c = 0 is a quadratic equation where a , b , c belongs to the real number a ≠ 0 then check a x 2 + c = 0 is a quadratic equation or not. Give reason

We know that a x 2 + b x + c is a two-degree polynomial in one variable (where a , b , c are real numbers and a ≠ 0 ). It is known as a quadratic polynomial. If we equate this quadratic polynomial equal zero it becomes a quadratic equation. Given equation is a x 2 + c = 0 , where a , c are real number and a ≠ 0 . On comparing the given equation with a x 2 + b x + c = 0 we get, a x 2 + 0 x + c = 0 Therefore, the equation a x 2 + c = 0 is a quadratic equation.

If a x 2 + b x + c = 0 is a quadratic equation where a , b , c belongs to the real number a ≠ 0 then check a x 2 = 0 is a quadratic equation or not. Give reason

We know that a x 2 + b x + c is a two-degree polynomial in one variable (where a , b , c are real numbers and a ≠ 0 ). It is known as a quadratic polynomial. If we equate this quadratic polynomial equal zero it becomes a quadratic equation. Given equation is a x 2 = 0 , where a is real number and a ≠ 0 . On comparing the given equation with a x 2 + b x + c = 0 we get, a x 2 + 0 x + 0 = 0 Therefore, the equation a x 2 = 0 is a quadratic equation.

Definition of rational number Q is given below: Q = p q , where p , q ∈ I and q ≠ 0 Write the definition of Rational Number in words.

According to the question The definition of a rational number Q is Q = p q where p , q ∈ I and q ≠ 0 We can write the definition of rational number in words. Any number is written in the form of p q where p , q belongs to integer and q is not equal to zero then the number is called a rational number.

Definition of rational number Q is given below. Q = p q , where p , q ∈ I and q ≠ 0 Is 6 0 a rational number?

According to the question The definition of a rational number Q is Q = p q where p , q ∈ I and q ≠ 0 We can write the definition of rational number in words. Any number is written in the form of p q where p , q belongs to integer and q is not equal to zero then the number is called a rational number. Now 6 0 is not a rational number because the denominator is zero.

Definition of rational number Q is given below. Q = p q , where p , q ∈ I and q ≠ 0 If p 2 + 7 q 2 - 25 is a rational expression, then here 5 and - 5 cannot be the values of q (Use definition)

Given mathematical statement: Q = p q , where p , q ∈ I and q ≠ 0 Now, consider Q = p 2 + 7 q 2 - 25 ....... 1 On putting q = 5 in eq 1 , we get Q = p 2 + 7 5 2 - 25 = p 2 + 7 25 - 25 = p 2 + 7 0 = ∞ But, for Q to be rational number, q ≠ 0 . So, Q = p 2 + 7 q 2 - 25 is a rational number when q is not equal to 5 . Similarly, on putting q = - 5 in eq 1 , we get Q = p 2 + 7 - 5 2 - 25 = p 2 + 7 25 - 25 = p 2 + 7 0 = ∞ Again, for Q to be rational number, q ≠ 0 . So, Q = p 2 + 7 q 2 - 25 is a rational number when q is not equal to - 5 . Hence, p 2 + 7 q 2 - 25 is a rational expression when q ∈ I - 5 , - 5 .