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Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals?
Yes, it is possible for a quadratic equation to have distinct irrational coefficients while having rational roots. For example, consider the quadratic equation (x^2 - \sqrt{2}x - \sqrt{3} = 0). The coefficients (-\sqrt{2}) and (-\sqrt{3}) are distinct irrationals, yet the roots of this equation can be rational. Specifically, if we apply the quadratic formula, we can find rational roots depending on the specific values of the coefficients.
Does transcendental mean it is equal to the ratio of two integers in math?
yes * * * * * No it does not. A transcendental number is not rational. It is irrational but, further than that, it is not the root of any polynomial equation with rational coefficients.
When the discriminant is perfect square the answer to a quadratic equation will be?
Rational.
What is the solution of rational equations reducible to quadratic equation?
A quadratic equation ax2 + bx + c = 0 has the solutions x = [-b +/- sqrt(b2 - 4*a*c)]/(2*a)
How do you work out 3x squared -10x equals -5?
This is a quadratic expression in x. It cannot be solved because it is an expression: there is no equation to solve. Furthermore, the discriminant for the quadratic = (-10)2 - 4*3*(-5) = 100+60 = 160 which is not a square number. There are, therefore no rational factors. While it would be possible to give irrational factors, factorising a quadratic into linear terms containing irrational numbers is rarely useful.
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals?
Yes, it is possible for a quadratic equation to have distinct irrational coefficients while having rational roots. For example, consider the quadratic equation (x^2 - \sqrt{2}x - \sqrt{3} = 0). The coefficients (-\sqrt{2}) and (-\sqrt{3}) are distinct irrationals, yet the roots of this equation can be rational. Specifically, if we apply the quadratic formula, we can find rational roots depending on the specific values of the coefficients.
Does transcendental mean it is equal to the ratio of two integers in math?
yes * * * * * No it does not. A transcendental number is not rational. It is irrational but, further than that, it is not the root of any polynomial equation with rational coefficients.
When the discriminant is perfect square the answer to a quadratic equation will be?
Rational.
How do you factor a polynomial with the equation of 6A2 - B 2?
The given polynomial does not have factors with rational coefficients.
Pi is transcendental What does this mean?
Real but not a root of an algebraic equation with rational roots coefficients
Is 4.6 irrational or rational?
4.6 is rational.
Is 37.5 a rational or irrational number?
Rational
What is an algebraic number?
An algebraic number is a complex number which is the root of a polynomial equation with rational coefficients.
What is the solution of rational equations reducible to quadratic equation?
A quadratic equation ax2 + bx + c = 0 has the solutions x = [-b +/- sqrt(b2 - 4*a*c)]/(2*a)
How do you work out 3x squared -10x equals -5?
This is a quadratic expression in x. It cannot be solved because it is an expression: there is no equation to solve. Furthermore, the discriminant for the quadratic = (-10)2 - 4*3*(-5) = 100+60 = 160 which is not a square number. There are, therefore no rational factors. While it would be possible to give irrational factors, factorising a quadratic into linear terms containing irrational numbers is rarely useful.
What does transcendental mean in mathematics?
An algebraic number is one which is a root of a polynomial equation with rational coefficients. All rational numbers are algebraic numbers. Irrational numbers such as square roots, cube roots, surds etc are algebraic but there are others that are not. A transcendental number is such a number: an irrational number that is not an algebraic number. pi and e (the base of the exponential function) are both transcendental.
Is 34.5 rational or irrational?
is 34.54 and irrational or rational. number
